663 Sentences With "estimator" | Random Sentence Generator

He was a construction estimator and she was a photographer.

The Education Department offers a repayment estimator on its website.

The Education Department's repayment estimator tool can tell you whether you're eligible.

The new estimator replaces the tax withholding calculator the agency previously offered.

The Department of Education offers a payment estimator tool on its website.

The Education Department's repayment estimator tool can tell you whether you're eligible.

Retirement Estimator is one of 11 online calculators available on the SSA's website.

Ms. Cheng recommends using the Education Department's online payment estimator for federal loans.

His father is an estimator with South River Restoration in Grand Prairie, Tex.

The estimator can't even take the time to find a clean sheet of paper.

The Social Security Administration's retirement estimator gives forecasts based on your actual earnings record.

And you may find that Airbnb's built-in estimator is pretty basic and vague.

WELCOME to the home page of EAGLE, the Economist Advantage in Golf Likelihood Estimator.

The I.R.S. W-4 online withholding estimator can help you fill out the form.

Using Uber's helpful fare estimator, taking an UberX along your homeward route at 6.30 p.m.

But EAGLE (Economist Advantage in Golf Likelihood Estimator), our new golf prediction system, is unimpressed.

Genworth has a good state-by-state estimator for this and other elder-care costs.

Use the Department of Education's repayment estimator to see which income-driven plans you qualify for.

Check out Federal Student Aid's Repayment Estimator tool to see what you'd pay on each plan.

The IRS warns users of its estimator tool that they should revisit their withholding in 2020.

The bride's father is a senior estimator at the Massman Construction Company in Overland Park, Kan.

Use a tax refund estimator to find out how much you could get backH&R Block has a super simple tax refund estimator that takes just a few minutes to complete — you don&apost have to sign up for an account or pay for anything up front.

There are also tax estimator calculators available online at the IRS website, or at H&R Block.

The estimator can result in a fairly wide range, but at the very least serves as a guidepost.

The latter would rather have a conversation about home values without the Redfin estimator having colored clients' expectations.

Federal borrowers can also use the Education Department's student loan estimator, which will help calculate their total monthly payments.

So I plan on updating this estimator when there is a major market shift (or when I get more data).

What to do: Gather your recent pay stubs and last year's tax return to use the IRS' tax withholding estimator.

"It was like he died again today," said Randy Lozano, 40, a sales estimator and Mr. Luna's brother-in-law.

Still, Glassdoor, which operates in the UK, has most of these features already, including a salary estimator and single tap saves.

Check out the Department of Education's repayment estimator to compare what your monthly payments would be under income-driven repayment plans.

To help get an idea of what they can expect for a payout, thredUP has a payout estimator for the public.

To see what your monthly payments would be under the different programs, you can use the Education Department's repayment estimator tool.

Uber is updating its app for drivers to include an "earnings estimator" to help drivers better keep track of their money.

Though the car didn't actually lose any range, the estimator would say it could go another ten miles—and then power down.

At the beginning of October, a 31-year-old construction estimator named Samantha parked her Honda Fit on the street in Chicago.

Apple will also display an interest estimator to show how much money you'll owe in interest if you let your balance add up.

Williams raised her daughter as a single parent and for years commuted to San Francisco, where she worked as a commercial glass estimator.

Since 272 The Economist has produced a statistical prediction model for men's major golf tournaments called EAGLE (Economist Advantage in Golf Likelihood Estimator).

He was a tough guy — he worked as an estimator for a local builder and constructed his own house pretty much single-handedly.

The withholding estimator asks detailed questions, so it's helpful to have last year's tax return handy along with your most recent pay stub.

The Economist Advantage in Golf Likelihood Estimator (EAGLE), our statistical forecasting system first developed last year, is poised to return for its third tournament.

Building a Series A SaaS valuation estimator (22009 edition) I've been hearing a lot lately about "The New Normal" for VC-backed technology companies.

Then go to the Internal Revenue Service's tax withholding estimator tool online, which will provide instructions on how to fill out your W-4.

In December — continuing the Israeli adtech invasion — SimilarWeb, a traffic estimator tool based in Tel Aviv, bought Quettra, a mobile analytics and measurement tools provider.

"The new estimator takes a new approach and makes it easier for taxpayers to review their withholding," said Charles Rettig, IRS commissioner, in a statement.

To see if your home is in a lower-risk area and what your premium might be, enter your address into FEMA's online premium estimator.

T-Mobile told Wireless Estimator the delayed purchase orders represented the telecom managing its capital expenditure and was not a nationwide shutdown on new infrastructure.

The I.R.S. recommends that workers complete a "paycheck checkup," by using the I.R.S.'s online estimator, to see if they need to adjust their withholdings.

The I.R.S. says the most accurate way to determine withholding for someone with multiple jobs or a working spouse is to use the I.R.S. estimator.

We are pleased to announce the release of EAGLE, the Economist Advantage in Golf Likelihood Estimator (backronyms have become de rigueur in the sports-forecasting world).

"The new estimator takes a new approach and makes it easier for taxpayers to review their withholding," said IRS Commissioner Charles Rettig in a news release.

In-state tuition and fees for Arizona State University students, for example, costs $10,792 for the current year, according to a cost estimator on ASU's website.

The Institute for College Access and Success summarizes the options on its income-based repayment website, or you can visit the Education Department's student loan estimator.

"Right there you can use the repayment estimator, which will give you an idea of what your payments will be and who your servicer is," says Rubin.

August 10th 203: LAST summer we unveiled the inaugural edition of EAGLE (Economist Advantage in Golf Likelihood Estimator), our statistical-projection system for men's major golf tournaments.

The I.R.S.'s Tax Withholding Estimator will be updated again soon, and that'll be the time to make sure you're on track for the 2020 tax year.

Glancing at Windows 03s battery life estimator on the 15-inch Notebook 9, I was promised 3 hours and 22 minutes off a remaining charge of 23 percent.

The mobile-friendly estimator is currently accurate only for 2019; the I.R.S. expects it to be updated for the 2020 tax year after the first of the year.

McKay, who works as an estimator, prefers to meet women in person because he doesn't think his personality and sense of humor translate well online and through dating apps.

The plans' rules and criteria vary, so Ms. Asher advises using the federal Repayment Estimator to see which plans you qualify for and what the monthly payment would be.

A Google rep told TechCrunch that the decision was "based on strong user feedback" and the calorie estimator will no longer appear in Google Maps for iOS starting this evening.

For "maximum accuracy and privacy," the IRS recommends using its Tax Withholding Estimator to determine the amount that should be withheld based on your income for one or more jobs.

The IRS recently made a round of updates to its tax withholding estimator, which you can use to figure out the amount of federal income tax held from your paycheck.

Once you have your W-2 or 1099 forms, it&aposll take less than five minutes to estimate your tax refund using H&R Block&aposs free tax refund estimator.

She is a daughter of Shelly J. Danni and Peter F. Danni of Allentown, Pa. The bride's father is a retired electrical estimator for the GC Electric Company in Allentown.

He has been talking to another local company, which is interested in training him to become an estimator — a salaried job that would pay more and offer room for advancement.

EAGLE (Economist Advantage in Golf Likelihood Estimator), our prediction model for men's major golf tournaments, ignores competitors' results and relies on players' personal scoring records, adjusted for course conditions and difficulty.

The IRS recently launched its new tax withholding estimator, a tool that aims to help filers narrow down the amount of federal income tax they should have pulled from their paychecks.

To address those concerns, the form allows workers to use the I.R.S.'s online tax withholding estimator tool or to complete a printed work sheet to determine how much to withhold.

But Glassdoor's Know Your Worth™ salary estimator can give you a much better sense of how your paycheck stacks up by providing a reference point for you to compare against.

All parents are expected to contribute at least $5,000 each year, and a cost estimator provided by the school allows families to find out how much a Dartmouth education will run them.

"The AI Auto Damage Estimator app technology was trained using anonymized claims photos so the software could be built," wrote Ted Kwartler, the assistant vice president of Liberty Mutual Innovation, in an email.

Vlad Rudolf, the chief estimator at a Queens-based company that makes custom awnings, said he routinely received requests for awnings with building names, not numbers, perhaps because it somehow seems more upscale.

To help SaaS founders get a more accurate sense of valuation for their Series A funding, I've set out to create a funding estimator that lays out the major variables that affect valuation amounts.

Andrew, an Eagle Scout who worked as an estimator for AsTech, regularly found stray animals and took them to the vet before taking them home to care for them, his mother, JoDell Pasek, tells PEOPLE.

The IRS kicked off the new year with a revamp of its tax withholding estimator tool, a calculator that helps you fine-tune the amount of federal income taxes that are pulled from your paycheck.

It shows commuters a range of public and private travel options, linking to bus and train, a taxi fare estimator, airport shuttle, car rental, ride-hailing alternative, bike sharing and space availability at designated parking garages.

Redfin, an internet real estate firm in Seattle, introduced its own home value estimator less than two years ago, commissioning an independent study that showed its figures were more accurate than Zillow's (Zillow disputes its conclusions).

T-Mobile notified some of the wireless contractors it works with that it would be delaying purchase orders for new infrastructure and 5G upgrades until 2020, unless the contractors already had the project materials, according to Wireless Estimator.

Ed Zarenski, a construction economics analyst with three decades of experience as a building projects cost estimator, said he arrived at those figures by first approximating the total cost of various materials involved, such as concrete, steel and temporary roads.

Ethan Brackenbury, a cost estimator for the federal Department of Energy in southeastern Washington State, said that he didn't like the idea of a trade war, and that he hadn't noticed any gain from the tax cut in his paycheck.

Underwriters could pursue similar occupations such as loan officer, which pays a slightly lower wage of $64,660 a year, but is projected to grow by 11 percent, or cost estimator, which pays $63,110 and will also grow by 11 percent.

Swiss Precision Diagnostics, the maker of the Clearblue Advanced Pregnancy Test with Weeks Estimator, used deceptive packaging and advertisements to mislead women into thinking the product measures gestational age in the same way a doctor would, a U.S. appeals court held Thursday.

"I'm not anti-union at all, but it's amazing how much they dictate everything that happens on a job in New York," said Jim Peregoy, a Missouri-based cost estimator who has worked on 853 projects in 27 states, including the Second Avenue subway.

No, of course not — but the cost of an Uber ride for that same span is roughly $70 to $90 according to a third-party fare estimator, and the price can go even higher depending on demand, so it's actually not that much of a stretch.

The difference between Hendricks' and Lester's ERA and FIP (fielding independent pitching), an ERA estimator that attempts to isolate those aspect of pitching for which the pitcher himself is responsible, is more than a run each, with Hendricks gaining more than any other pitcher in the league.

I haven't been able to put it through its paces yet, but in my experience with it last night, I kept neurotically checking the battery life estimator and it kept throwing up figures close to 21 hours, even on a laptop that was two-thirds charged and not sitting idle.

Here are a few examples: Of course, this a fairly broad estimator and it won't be tough to find outliers that break the formula — but, in general, it should lead to generating valuation ranges that could help SaaS founders wrap their heads around what is possible and what they should aim for with their first round of venture capital funding.

Pricing is determined by a number of factors, including the estimated retail price, brand, seasonality, and quality of each item, and there's handy estimator tool on Thredup's website so you can get an idea of just how much $$$ you're in for (and while you're at it, check out the footprint calculator to assess how your personal shopping behaviors affect the planet).

So, we expect that the biased estimator underestimates σ2 by σ2/n, and so the biased estimator = (1 − 1/n) × the unbiased estimator = (n − 1)/n × the unbiased estimator.

The process of transforming an estimator using the Rao–Blackwell theorem is sometimes called Rao–Blackwellization. The transformed estimator is called the Rao–Blackwell estimator.

Compared to the maximum-likelihood estimator under the equiprobable population, this estimator is very efficient.

In statistics, Hodges' estimator (or the Hodges–Le Cam estimator), named for Joseph Hodges, is a famous counterexample of an estimator which is "superefficient", i.e. it attains smaller asymptotic variance than regular efficient estimators. The existence of such a counterexample is the reason for the introduction of the notion of regular estimators. Hodges' estimator improves upon a regular estimator at a single point.

This estimate is based on coalescent theory. Watterson's estimator is commonly used for its simplicity. When its assumptions are met, the estimator is unbiased and the variance of the estimator decreases with increasing sample size or recombination rate. However, the estimator can be biased by population structure.

In general, any superefficient estimator may surpass a regular estimator at most on a set of Lebesgue measure zero.

For univariate distributions that are symmetric about one median, the Hodges–Lehmann estimator is a robust and highly efficient estimator of the population median; for non-symmetric distributions, the Hodges–Lehmann estimator is a robust and highly efficient estimator of the population pseudo-median, which is the median of a symmetrized distribution and which is close to the population median. The Hodges–Lehmann estimator has been generalized to multivariate distributions.

The Cramér–Rao lower bound is a lower bound of the variance of an unbiased estimator, representing the "best" an unbiased estimator can be. An efficient estimator is also the minimum variance unbiased estimator (MVUE). This is because an efficient estimator maintains equality on the Cramér–Rao inequality for all parameter values, which means it attains the minimum variance for all parameters (the definition of the MVUE). The MVUE estimator, even if it exists, is not necessarily efficient, because "minimum" does not mean equality holds on the Cramér–Rao inequality.

Bias is a property of the estimator, not of the estimate. Often, people refer to a "biased estimate" or an "unbiased estimate," but they really are talking about an "estimate from a biased estimator," or an "estimate from an unbiased estimator." Also, people often confuse the "error" of a single estimate with the "bias" of an estimator. That the error for one estimate is large, does not mean the estimator is biased.

The average salary of a Civil Estimator normally falls within the following categories: :Trainee Estimator – £12,000 to £18,000 per annum. :Junior Estimator – £18,000 to £28,000 per annum. :Senior Estimator – £25,000 to £500,00 per annum. In addition to the above salaries, civil estimators often have further incentives from cash rewards and a bonus system as an OTE.

A number of alternative estimators of the odds ratio have been proposed to address limitations of the sample odds ratio. One alternative estimator is the conditional maximum likelihood estimator, which conditions on the row and column margins when forming the likelihood to maximize (as in Fisher's exact test). Another alternative estimator is the Mantel–Haenszel estimator.

An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).

Efficiency in statistics is important because they allow one to compare the performance of various estimators. Although an unbiased estimator is usually favored over a biased one, a more efficient biased estimator can sometimes be more valuable than a less efficient unbiased estimator. For example, this can occur when the values of the biased estimator gathers around a number closer to the true value. Thus, estimator performance can be predicted easily by comparing their mean squared errors or variances.

For T>2, they are not. If the error terms u_{it} are homoskedastic with no serial correlation, the fixed effects estimator is more efficient than the first difference estimator. If u_{it} follows a random walk, however, the first difference estimator is more efficient.

This always consists of scaling down the unbiased estimator (dividing by a number larger than n − 1), and is a simple example of a shrinkage estimator: one "shrinks" the unbiased estimator towards zero. For the normal distribution, dividing by n + 1 (instead of n − 1 or n) minimizes mean squared error. The resulting estimator is biased, however, and is known as the biased sample variation.

The improved estimator is unbiased if and only if the original estimator is unbiased, as may be seen at once by using the law of total expectation. The theorem holds regardless of whether biased or unbiased estimators are used. The theorem seems very weak: it says only that the Rao–Blackwell estimator is no worse than the original estimator. In practice, however, the improvement is often enormous.

Most often, trimmed estimators are used for parameter estimation of the same parameter as the untrimmed estimator. In some cases the estimator can be used directly, while in other cases it must be adjusted to yield an unbiased consistent estimator. For example, when estimating a location parameter for a symmetric distribution, a trimmed estimator will be unbiased (assuming the original estimator was unbiased), as it removes the same amount above and below. However, if the distribution has skew, trimmed estimators will generally be biased and require adjustment.

In estimation theory, the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data.

The James–Stein estimator is a biased estimator of the mean of Gaussian random vectors. It can be shown that the James–Stein estimator dominates the "ordinary" least squares approach, i.e., it has lower mean squared error. It is the best-known example of Stein's phenomenon.

Sufficiency finds a useful application in the Rao–Blackwell theorem, which states that if g(X) is any kind of estimator of θ, then typically the conditional expectation of g(X) given sufficient statistic T(X) is a better estimator of θ, and is never worse. Sometimes one can very easily construct a very crude estimator g(X), and then evaluate that conditional expected value to get an estimator that is in various senses optimal.

This holds even under heteroscedasticity. More precisely, the OLS estimator in the presence of heteroscedasticity is asymptotically normal, when properly normalized and centered, with a variance- covariance matrix that differs from the case of homoscedasticity. In 1980, White proposed a consistent estimator for the variance-covariance matrix of the asymptotic distribution of the OLS estimator. This validates the use of hypothesis testing using OLS estimators and White's variance-covariance estimator under heteroscedasticity.

The second equation follows since θ is measurable with respect to the conditional distribution P(x\mid\theta). An estimator is said to be unbiased if its bias is equal to zero for all values of parameter θ, or equivalently, if the expected value of the estimator matches that of the parameter. In a simulation experiment concerning the properties of an estimator, the bias of the estimator may be assessed using the mean signed difference.

Since the expected value of an unbiased estimator is equal to the parameter value, E[T]=\theta. Therefore, MSE(T)=Var(T) as the (E[T]-\theta)^2 term drops out from being equal to 0. If an unbiased estimator of a parameter θ attains e(T) = 1 for all values of the parameter, then the estimator is called efficient. Equivalently, the estimator achieves equality in the Cramér–Rao inequality for all θ.

In statistics, Stein's unbiased risk estimate (SURE) is an unbiased estimator of the mean-squared error of "a nearly arbitrary, nonlinear biased estimator." In other words, it provides an indication of the accuracy of a given estimator. This is important since the true mean-squared error of an estimator is a function of the unknown parameter to be estimated, and thus cannot be determined exactly. The technique is named after its discoverer, Charles Stein.

Seeing the James–Stein estimator as an empirical Bayes method gives some intuition to this result: One assumes that θ itself is a random variable with prior distribution \sim N(0, A), where A is estimated from the data itself. Estimating A only gives an advantage compared to the maximum-likelihood estimator when the dimension m is large enough; hence it does not work for m\leq 2. The James–Stein estimator is a member of a class of Bayesian estimators that dominate the maximum-likelihood estimator. A consequence of the above discussion is the following counterintuitive result: When three or more unrelated parameters are measured, their total MSE can be reduced by using a combined estimator such as the James–Stein estimator; whereas when each parameter is estimated separately, the least squares (LS) estimator is admissible.

An estimator based on the minimum of an additive process can be applied to image processing. Such estimator aims to distinguish between real signal and noise in the picture pixels.

In 1988, Robinson applied Nadaraya-Waston kernel estimator to test the nonparametric element to build a least-squares estimator After that, in 1997, local linear method was found by Truong.

Rao–Blackwellization is an idempotent operation. Using it to improve the already improved estimator does not obtain a further improvement, but merely returns as its output the same improved estimator.

In statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation. This is generally done to obtain a more robust statistic, and the extreme values are considered outliers. Trimmed estimators also often have higher efficiency for mixture distributions and heavy-tailed distributions than the corresponding untrimmed estimator, at the cost of lower efficiency for other distributions, such as the normal distribution. Given an estimator, the n% trimmed version is obtained by discarding the n% lowest and highest observations: it is a statistic on the middle of the data.

Two naturally desirable properties of estimators are for them to be unbiased and have minimal mean squared error (MSE). These cannot in general both be satisfied simultaneously: a biased estimator may have lower mean squared error (MSE) than any unbiased estimator; see estimator bias. Among unbiased estimators, there often exists one with the lowest variance, called the minimum variance unbiased estimator (MVUE). In some cases an unbiased efficient estimator exists, which, in addition to having the lowest variance among unbiased estimators, satisfies the Cramér–Rao bound, which is an absolute lower bound on variance for statistics of a variable.

In statistics, the Hodges–Lehmann estimator is a robust and nonparametric estimator of a population's location parameter. For populations that are symmetric about one median, such as the (Gaussian) normal distribution or the Student t-distribution, the Hodges–Lehmann estimator is a consistent and median-unbiased estimate of the population median. For non-symmetric populations, the Hodges–Lehmann estimator estimates the "pseudo–median", which is closely related to the population median. The Hodges–Lehmann estimator was proposed originally for estimating the location parameter of one-dimensional populations, but it has been used for many more purposes.

In statistics, an adaptive estimator is an estimator in a parametric or semiparametric model with nuisance parameters such that the presence of these nuisance parameters does not affect efficiency of estimation.

In statistics, the delta method is a result concerning the approximate probability distribution for a function of an asymptotically normal statistical estimator from knowledge of the limiting variance of that estimator.

The ratio estimator (RE- estimator) of the tail-index was introduced by Goldie and Smith.Goldie C.M., Smith R.L. (1987) Slow variation with remainder: theory and applications. Quart. J. Math. Oxford, v.

The Hodges–Lehmann estimator was proposed in 1963 independently by Pranab Kumar Sen and by Joseph Hodges and Erich Lehmann, and so it is also called the "Hodges–Lehmann–Sen estimator".

The Kaplan–Meier estimator can be used to estimate the survival function. The Nelson–Aalen estimator can be used to provide a non-parametric estimate of the cumulative hazard rate function.

A biased estimator may be used for various reasons: because an unbiased estimator does not exist without further assumptions about a population; because an estimator is difficult to compute (as in unbiased estimation of standard deviation); because an estimator is median-unbiased but not mean-unbiased (or the reverse); because a biased estimator gives a lower value of some loss function (particularly mean squared error) compared with unbiased estimators (notably in shrinkage estimators); or because in some cases being unbiased is too strong a condition, and the only unbiased estimators are not useful. Further, mean-unbiasedness is not preserved under non-linear transformations, though median-unbiasedness is (see ); for example, the sample variance is a biased estimator for the population variance. These are all illustrated below.

A consistent estimator is one for which, when the estimate is considered as a random variable indexed by the number n of items in the data set, as n increases the estimates converge in probability to the value that the estimator is designed to estimate. An estimator that has Fisher consistency is one for which, if the estimator were applied to the entire population rather than a sample, the true value of the estimated parameter would be obtained.

In econometrics, the Arellano–Bond estimator is a generalized method of moments estimator used to estimate dynamic models of panel data. It was proposed in 1991 by Manuel Arellano and Stephen Bond, based on the earlier work by Alok Bhargava and John Denis Sargan in 1983, for addressing certain endogeneity problems. The GMM-SYS estimator is a system that contains both the levels and the first difference equations. It provides an alternative to the standard first difference GMM estimator.

The median of the natural logarithms of a sample is a robust estimator of \mu. The median absolute deviation of the natural logarithms of a sample is a robust estimator of \sigma.

In the previous section the least squares estimator \hat\beta was obtained as a value that minimizes the sum of squared residuals of the model. However it is also possible to derive the same estimator from other approaches. In all cases the formula for OLS estimator remains the same: ; the only difference is in how we interpret this result.

The realized kernel (RK) is an estimator of volatility. The estimator is typically computed with high frequency return data, such as second-by-second returns. Unlike the realized variance, the realized kernel is a robust estimator of volatility, in the sense that the realized kernel estimates the appropriate volatility quantity, even when the returns are contaminated with noise.

In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation.

An earlier version of the estimator was developed by Charles Stein in 1956, and is sometimes referred to as Stein's estimator. The result was improved by Willard James and Charles Stein in 1961.

Therefore, the estimator is approximately unbiased for large sample sizes.

See invariant estimator for background on invariance or see equivariance.

In statistical theory, the Pitman closeness criterion, named after E. J. G. Pitman, is a way of comparing two candidate estimators for the same parameter. Under this criterion, estimator A is preferred to estimator B if the probability that estimator A is closer to the true value than estimator B is greater than one half. Here the meaning of closer is determined by the absolute difference in the case of a scalar parameter, or by the Mahalanobis distance for a vector parameter.

In general, the spread of an estimator around the parameter θ is a measure of estimator efficiency and performance. This performance can be calculated by finding the mean squared error: Let T be an estimator for the parameter θ. The mean squared error of T is the value MSE(T)=E[(T-\theta)^2]. Here, MSE(T)=E[(T-\theta)^2]=E[(T-E[T]+E[T]-\theta)^2] =E[(T-E[T])^2]+2E[T-E[T (E[T]-\theta)+(E[T]-\theta))^2 =Var(T)+(E[T]-\theta)^2 Therefore, an estimator T1 performs better than an estimator T2 if MSE(T_1).

In statistics, the Rao–Blackwell theorem, sometimes referred to as the Rao–Blackwell–Kolmogorov theorem, is a result which characterizes the transformation of an arbitrarily crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria. The Rao–Blackwell theorem states that if g(X) is any kind of estimator of a parameter θ, then the conditional expectation of g(X) given T(X), where T is a sufficient statistic, is typically a better estimator of θ, and is never worse. Sometimes one can very easily construct a very crude estimator g(X), and then evaluate that conditional expected value to get an estimator that is in various senses optimal. The theorem is named after Calyampudi Radhakrishna Rao and David Blackwell.

This section presents two examples of calculating the maximum spacing estimator.

In statistics and signal processing, the orthogonality principle is a necessary and sufficient condition for the optimality of a Bayesian estimator. Loosely stated, the orthogonality principle says that the error vector of the optimal estimator (in a mean square error sense) is orthogonal to any possible estimator. The orthogonality principle is most commonly stated for linear estimators, but more general formulations are possible. Since the principle is a necessary and sufficient condition for optimality, it can be used to find the minimum mean square error estimator.

To date, there is not currently a professional qualification or regulatory body for civils estimating within the UK. As a consequence, the learning curve from a trainee estimator to senior estimator could be an undisclosed amount of time and largely falls into the responsibility of the employer and or senior estimator to determine time scale and progression of trainee estimators.

As stated above, for univariate parameters, median-unbiased estimators remain median-unbiased under transformations that preserve order (or reverse order). Note that, when a transformation is applied to a mean-unbiased estimator, the result need not be a mean-unbiased estimator of its corresponding population statistic. By Jensen's inequality, a convex function as transformation will introduce positive bias, while a concave function will introduce negative bias, and a function of mixed convexity may introduce bias in either direction, depending on the specific function and distribution. That is, for a non-linear function f and a mean-unbiased estimator U of a parameter p, the composite estimator f(U) need not be a mean-unbiased estimator of f(p).

Other methods of estimating a ratio estimator include maximum likelihood and bootstrapping.

Redescending M-estimators have high breakdown points (close to 0.5), and their Ψ function can be chosen to redescend smoothly to 0. This means that moderately large outliers are not ignored completely, and greatly improves the efficiency of the redescending M-estimator. The redescending M-estimators are slightly more efficient than the Huber estimator for several symmetric, wider tailed distributions, but about 20% more efficient than the Huber estimator for the Cauchy distribution. This is because they completely reject gross outliers, while the Huber estimator effectively treats these the same as moderate outliers.

However, it finds some use in special cases: it is the maximally efficient estimator for the center of a uniform distribution, trimmed mid-ranges address robustness, and as an L-estimator, it is simple to understand and compute.

Stein's example is surprising, since the "ordinary" decision rule is intuitive and commonly used. In fact, numerous methods for estimator construction, including maximum likelihood estimation, best linear unbiased estimation, least squares estimation and optimal equivariant estimation, all result in the "ordinary" estimator. Yet, as discussed above, this estimator is suboptimal. To demonstrate the unintuitive nature of Stein's example, consider the following real-world example.

The fixed effect assumption is that the individual-specific effects are correlated with the independent variables. If the random effects assumption holds, the random effects estimator is more efficient than the fixed effects estimator. However, if this assumption does not hold, the random effects estimator is not consistent. The Durbin–Wu–Hausman test is often used to discriminate between the fixed and the random effects models.

Here, we show two derivations of the Kaplan–Meier estimator. Both are based on rewriting the survival function in terms of what is sometimes called hazard, or mortality rates. However, before doing this it is worthwhile to consider a naive estimator.

In statistics, Fisher consistency, named after Ronald Fisher, is a desirable property of an estimator asserting that if the estimator were calculated using the entire population rather than a sample, the true value of the estimated parameter would be obtained.

Finally, note that because the variables x and y are jointly Gaussian, the minimum MSE estimator is linear.See the article minimum mean square error. Therefore, in this case, the estimator above minimizes the MSE among all estimators, not only linear estimators.

Bias is a distinct concept from consistency. Consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased; see bias versus consistency for more. All else being equal, an unbiased estimator is preferable to a biased estimator, although in practice, biased estimators (with generally small bias) are frequently used. When a biased estimator is used, bounds of the bias are calculated.

Chapman and Hall, 1994. local Whittle's estimator, wavelet analysis,R. H. Riedi. Multifractal processes.

In statistics, a k-statistic is a minimum-variance unbiased estimator of a cumulant.

A Bayesian analog is a Bayes estimator, particularly with minimum mean square error (MMSE).

The scoring algorithm is an iterative method for numerically determining the maximum likelihood estimator.

The M-estimating equation for a redescending estimator may not have a unique solution.

This is of course absurd; we have not obtained a better estimator for US wheat yield by itself, but we have produced an estimator for the vector of the means of all three random variables, which has a reduced total risk. This occurs because the cost of a bad estimate in one component of the vector is compensated by a better estimate in another component. Also, a specific set of the three estimated mean values obtained with the new estimator will not necessarily be better than the ordinary set (the measured values). It is only on average that the new estimator is better.

In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated. Since the posterior mean is cumbersome to calculate, the form of the MMSE estimator is usually constrained to be within a certain class of functions.

When the covariates are exogenous, the small-sample properties of the OLS estimator can be derived in a straightforward manner by calculating moments of the estimator conditional on X. When some of the covariates are endogenous so that instrumental variables estimation is implemented, simple expressions for the moments of the estimator cannot be so obtained. Generally, instrumental variables estimators only have desirable asymptotic, not finite sample, properties, and inference is based on asymptotic approximations to the sampling distribution of the estimator. Even when the instruments are uncorrelated with the error in the equation of interest and when the instruments are not weak, the finite sample properties of the instrumental variables estimator may be poor. For example, exactly identified models produce finite sample estimators with no moments, so the estimator can be said to be neither biased nor unbiased, the nominal size of test statistics may be substantially distorted, and the estimates may commonly be far away from the true value of the parameter.

Thus an efficient estimator need not exist, but if it does, it is the MVUE.

For example, the square root of the unbiased estimator of the population variance is not a mean-unbiased estimator of the population standard deviation: the square root of the unbiased sample variance, the corrected sample standard deviation, is biased. The bias depends both on the sampling distribution of the estimator and on the transform, and can be quite involved to calculate – see unbiased estimation of standard deviation for a discussion in this case.

A standard application of SURE is to choose a parametric form for an estimator, and then optimize the values of the parameters to minimize the risk estimate. This technique has been applied in several settings. For example, a variant of the James–Stein estimator can be derived by finding the optimal shrinkage estimator. The technique has also been used by Donoho and Johnstone to determine the optimal shrinkage factor in a wavelet denoising setting.

There are three caveats to consider regarding Bessel's correction: # It does not yield an unbiased estimator of standard deviation. # The corrected estimator often has a higher mean squared error (MSE) than the uncorrected estimator. Furthermore, there is no population distribution for which it has the minimum MSE because a different scale factor can always be chosen to minimize MSE. # It is only necessary when the population mean is unknown (and estimated as the sample mean).

The OLS estimator is identical to the maximum likelihood estimator (MLE) under the normality assumption for the error terms.[proof] This normality assumption has historical importance, as it provided the basis for the early work in linear regression analysis by Yule and Pearson. From the properties of MLE, we can infer that the OLS estimator is asymptotically efficient (in the sense of attaining the Cramér–Rao bound for variance) if the normality assumption is satisfied.

The winsorized mean is a useful estimator because it is less sensitive to outliers than the mean but will still give a reasonable estimate of central tendency or mean for almost all statistical models. In this regard it is referred to as a robust estimator.

Had the random variable x also been Gaussian, then the estimator would have been optimal. Notice, that the form of the estimator will remain unchanged, regardless of the apriori distribution of x, so long as the mean and variance of these distributions are the same.

So, the estimator of Var(∑X) becomes nS2X \+ n'''2 giving : standard error(''''') = √[(S2X \+ '''''2)/n].

He is an estimator/buyer by trade and is married to Sadie Gillett with three children.

Econometric theory uses statistical theory and mathematical statistics to evaluate and develop econometric methods. Econometricians try to find estimators that have desirable statistical properties including unbiasedness, efficiency, and consistency. An estimator is unbiased if its expected value is the true value of the parameter; it is consistent if it converges to the true value as the sample size gets larger, and it is efficient if the estimator has lower standard error than other unbiased estimators for a given sample size. Ordinary least squares (OLS) is often used for estimation since it provides the BLUE or "best linear unbiased estimator" (where "best" means most efficient, unbiased estimator) given the Gauss-Markov assumptions.

In statistics, the Gauss–Markov theorem states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. The errors do not need to be normal, nor do they need to be independent and identically distributed (only uncorrelated with mean zero and homoscedastic with finite variance). The requirement that the estimator be unbiased cannot be dropped, since biased estimators exist with lower variance. See, for example, the James–Stein estimator (which also drops linearity), ridge regression, or simply any degenerate estimator.

In statistics, the bias (or bias function) of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator. Bias can also be measured with respect to the median, rather than the mean (expected value), in which case one distinguishes median-unbiased from the usual mean-unbiasedness property.

The term consistency in statistics usually refers to an estimator that is asymptotically consistent. Fisher consistency and asymptotic consistency are distinct concepts, although both aim to define a desirable property of an estimator. While many estimators are consistent in both senses, neither definition encompasses the other. For example, suppose we take an estimator Tn that is both Fisher consistent and asymptotically consistent, and then form Tn + En, where En is a deterministic sequence of nonzero numbers converging to zero.

Efficiency of an estimator may change significantly if the distribution changes, often dropping. This is one of the motivations of robust statistics – an estimator such as the sample mean is an efficient estimator of the population mean of a normal distribution, for example, but can be an inefficient estimator of a mixture distribution of two normal distributions with the same mean and different variances. For example, if a distribution is a combination of 98% N(μ, σ) and 2% N(μ, 10σ), the presence of extreme values from the latter distribution (often "contaminating outliers") significantly reduces the efficiency of the sample mean as an estimator of μ. By contrast, the trimmed mean is less efficient for a normal distribution, but is more robust (less affected) by changes in distribution, and thus may be more efficient for a mixture distribution.

The Theil–Sen estimator is a method for robust linear regression based on finding medians of slopes..

Despite numerous contenders, the NFXP maximum likelihood estimator remains the leading estimation method for Markov decision models.

Thus, the sample mean is a finite-sample efficient estimator for the mean of the normal distribution.

The fixed effect assumption is that the individual specific effect is correlated with the independent variables. If the random effects assumption holds, the random effects estimator is more efficient than the fixed effects model. However, if this assumption does not hold, the random effects estimator is not consistent.

His research work is geared towards applications in biosciences. Aalen's early work on counting processes and martingales, starting with his 1976 Ph.D. thesis at the University of California, Berkeley, has had profound influence in biostatistics. Inferences for fundamental quantities associated with cumulative hazard rates, in survival analysis and models for analysis of event histories, are typically based on the Nelson–Aalen estimator or appropriate related statistics. The Nelson–Aalen estimator is related to the Kaplan-Meier estimator and generalisations thereof.

In statistics and econometrics, the maximum score estimator is a nonparametric estimator for discrete choice models developed by Charles Manski in 1975. Unlike the multinomial probit and multinomial logit estimators, it makes no assumptions about the distribution of the unobservable part of utility. However, its statistical properties (particularly its asymptotic distribution) are more complicated than the multinomial probit and logit models, making statistical inference difficult. To address these issues, Joel Horowitz proposed a variant, called the smoothed maximum score estimator.

Let F_u be their conditional excess distribution function. Pickands–Balkema–de Haan theorem (Pickands, 1975; Balkema and de Haan, 1974) states that for a large class of underlying distribution functions F, and large u, F_u is well approximated by the generalized Pareto distribution (GPD), which motivated Peak Over Threshold (POT) methods to estimate \xi: the GPD plays the key role in POT approach. A renowned estimator using the POT methodology is the Hill's estimator. Technical formulation of the Hill's estimator is as follows.

The choice of L-estimator and adjustment depend on the distribution whose parameter is being estimated. For example, when estimating a location parameter, for a symmetric distribution a symmetric L-estimator (such as the median or midhinge) will be unbiased. However, if the distribution has skew, symmetric L-estimators will generally be biased and require adjustment. For example, in a skewed distribution, the nonparametric skew (and Pearson's skewness coefficients) measure the bias of the median as an estimator of the mean.

A Bayes estimator derived through the empirical Bayes method is called an empirical Bayes estimator. Empirical Bayes methods enable the use of auxiliary empirical data, from observations of related parameters, in the development of a Bayes estimator. This is done under the assumption that the estimated parameters are obtained from a common prior. For example, if independent observations of different parameters are performed, then the estimation performance of a particular parameter can sometimes be improved by using data from other observations.

An estimator is Bayes if it minimizes the average risk : \int_\Theta R(\theta,\delta)\,d\Pi(\theta).

However, for some probability distributions, there is no guarantee that the least-squares solution is even possible given the observations; still, in such cases it is the best estimator that is both linear and unbiased. For example, it is easy to show that the arithmetic mean of a set of measurements of a quantity is the least-squares estimator of the value of that quantity. If the conditions of the Gauss–Markov theorem apply, the arithmetic mean is optimal, whatever the distribution of errors of the measurements might be. However, in the case that the experimental errors do belong to a normal distribution, the least-squares estimator is also a maximum likelihood estimator.

For the method of conditional probabilities to work, it suffices if the algorithm keeps the pessimistic estimator from decreasing (or increasing, as appropriate). The algorithm does not necessarily have to maximize (or minimize) the pessimistic estimator. This gives some flexibility in deriving the algorithm. The next two algorithms illustrate this. 1\.

The Horvitz–Thompson estimator is frequently applied in survey analyses and can be used to account for missing data.

The group means could be modeled as fixed or random effects for each grouping. In a fixed effects model each group mean is a group-specific fixed quantity. In panel data where longitudinal observations exist for the same subject, fixed effects represent the subject-specific means. In panel data analysis the term fixed effects estimator (also known as the within estimator) is used to refer to an estimator for the coefficients in the regression model including those fixed effects (one time-invariant intercept for each subject).

Stephen Bond is a British economist at Nuffield College, Oxford, Oxford, specialising in applied microeconometrics, particularly the investment and financial behaviour of firms. Together with Manuel Arellano, he developed the Arellano–Bond estimator, a widely used GMM estimator for panel data.RePEc lists the paper as the most cited article ever in economics.

Thus a Bayesian analysis might be undertaken, leading to a posterior distribution for relevant parameters, but the use of a specific utility or loss function may be unclear. Ideas of invariance can then be applied to the task of summarising the posterior distribution. In other cases, statistical analyses are undertaken without a fully defined statistical model or the classical theory of statistical inference cannot be readily applied because the family of models being considered are not amenable to such treatment. In addition to these cases where general theory does not prescribe an estimator, the concept of invariance of an estimator can be applied when seeking estimators of alternative forms, either for the sake of simplicity of application of the estimator or so that the estimator is robust.

It is for this reason that we have spelled out "sample skewness", etc., in the above formulas, to make it explicit that the user should choose the best estimator according to the problem at hand, as the best estimator for skewness and kurtosis depends on the amount of skewness (as shown by Joanes and Gill).

In information theory, given an unknown stationary source with alphabet A and a sample w from , the Krichevsky–Trofimov (KT) estimator produces an estimate pi(w) of the probability of each symbol i ∈ A. This estimator is optimal in the sense that it minimizes the worst-case regret asymptotically. For a binary alphabet and a string w with m zeroes and n ones, the KT estimator pi(w) is defined as:Krichevsky, R. E. and Trofimov V. K. (1981), "The Performance of Universal Encoding", IEEE Trans. Inf. Theory, Vol. IT-27, No. 2, pp. 199–207.

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. There are point and interval estimators. The point estimators yield single- valued results, although this includes the possibility of single vector-valued results and results that can be expressed as a single function. This is in contrast to an interval estimator, where the result would be a range of plausible values (or vectors or functions).

However, in some cases, no unbiased technique exists which achieves the bound. This may occur either if for any unbiased estimator, there exists another with a strictly smaller variance, or if an MVU estimator exists, but its variance is strictly greater than the inverse of the Fisher information. The Cramér–Rao bound can also be used to bound the variance of biased estimators of given bias. In some cases, a biased approach can result in both a variance and a mean squared error that are below the unbiased Cramér–Rao lower bound; see estimator bias.

Hannum et al. (2013). Hannum et al. adjusted their blood-based age estimator (by adjusting the slope and the intercept term) in order to apply it to other tissue types. Since this adjustment step removes differences between tissue, the blood-based estimator from Hannum et al. cannot be used to compare the ages of different tissues/organs.

Two-step M-estimators deals with M-estimation problems that require preliminary estimation to obtain the parameter of interest. Two-step M-estimation is different from usual M-estimation problem because asymptotic distribution of the second-step estimator generally depends on the first-step estimator. Accounting for this change in asymptotic distribution is important for valid inference.

Otherwise, the M-estimator is said to be of ρ-type. In most practical cases, the M-estimators are of ψ-type.

In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter. For practical statistics problems, it is important to determine the MVUE if one exists, since less-than-optimal procedures would naturally be avoided, other things being equal. This has led to substantial development of statistical theory related to the problem of optimal estimation. While combining the constraint of unbiasedness with the desirability metric of least variance leads to good results in most practical settings—making MVUE a natural starting point for a broad range of analyses—a targeted specification may perform better for a given problem; thus, MVUE is not always the best stopping point.

The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator (how widely spread the estimates are from one data sample to another) and its bias (how far off the average estimated value is from the true value). For an unbiased estimator, the MSE is the variance of the estimator. Like the variance, MSE has the same units of measurement as the square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root- mean-square error or root-mean-square deviation (RMSE or RMSD), which has the same units as the quantity being estimated; for an unbiased estimator, the RMSE is the square root of the variance, known as the standard error.

This means that the distributions of the estimates become more and more concentrated near the true value of the parameter being estimated, so that the probability of the estimator being arbitrarily close to θ0 converges to one. In practice one constructs an estimator as a function of an available sample of size n, and then imagines being able to keep collecting data and expanding the sample ad infinitum. In this way one would obtain a sequence of estimates indexed by n, and consistency is a property of what occurs as the sample size “grows to infinity”. If the sequence of estimates can be mathematically shown to converge in probability to the true value θ0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent.

As a result, with a sample size of 1, the maximum likelihood estimator for n will systematically underestimate n by (n − 1)/2.

Urn:nbn:se:kth:diva-218100 The resulting estimator can be shown to be strongly consistent and asymptotically normal and can be evaluated using relatively simple algorithms.

If one is instead interested in estimating an individual parameter, then using a combined estimator does not help and is in fact worse.

We retransform the square root of length of stay using a smearing estimator to obtain unbiased estimates of the effect of managed care.

However, any particular component (such as the speed of light) would improve for some parameter values, and deteriorate for others. Thus, although the James–Stein estimator dominates the LS estimator when three or more parameters are estimated, any single component does not dominate the respective component of the LS estimator. The conclusion from this hypothetical example is that measurements should be combined if one is interested in minimizing their total MSE. For example, in a telecommunication setting, it is reasonable to combine channel tap measurements in a channel estimation scenario, as the goal is to minimize the total channel estimation error.

In robust statistics, repeated median regression, also known as the repeated median estimator, is a robust linear regression algorithm. The estimator has a breakdown point of 50%. Although it is equivariant under scaling, or under linear transformations of either its explanatory variable or its response variable, it is not under affine transformations that combine both variables.Peter J. Rousseeuw, Nathan S. Netanyahu, and David M. Mount, "New Statistical and Computational Results on the Repeated Median Regression Estimator", in New Directions in Statistical Data Analysis and Robustness, edited by Stephan Morgenthaler, Elvezio Ronchetti, and Werner A. Stahel, Birkhauser Verlag, Basel, 1993, pp. 177-194.

If the relationship parameter \beta is estimated by regressing the observed y_i on x_i , the resulting ordinary least squares regression estimator is inconsistent. It will yield a downwards- biased estimate of the slope coefficient and an upward-biased estimate of the intercept. Takeshi Amemiya (1973) has proven that the maximum likelihood estimator suggested by Tobin for this model is consistent.

A quirky example would be estimating the speed of light, tea consumption in Taiwan, and hog weight in Montana, all together. The James–Stein estimator always improves upon the total MSE, i.e., the sum of the expected errors of each component. Therefore, the total MSE in measuring light speed, tea consumption, and hog weight would improve by using the James–Stein estimator.

Research on eyewitness testimony looks at systematic variables or estimator variables. Estimator variables are characteristics of the witness, event, testimony, or testimony evaluators. Systematic variables are variables that are, or have the possibility of, being controlled by the criminal justice system. Both sets of variables can be manipulated and studied during research, but only system variables can be controlled in actual procedure.

However, this estimator is biased when sample sizes are small or if they vary between populations. Therefore, more elaborate methods are used to compute FST in practice. Two of the most widely used procedures are the estimator by Weir & Cockerham (1984), or performing an Analysis of molecular variance. A list of implementations is available at the end of this article.

1 in Gourieroux, C. and Monfort, A. (1995). Statistics and econometric models, volume 1. Cambridge University Press. The term equivariant estimator is used in formal mathematical contexts that include a precise description of the relation of the way the estimator changes in response to changes to the dataset and parameterisation: this corresponds to the use of "equivariance" in more general mathematics.

Fisher information is widely used in optimal experimental design. Because of the reciprocity of estimator-variance and Fisher information, minimizing the variance corresponds to maximizing the information. When the linear (or linearized) statistical model has several parameters, the mean of the parameter estimator is a vector and its variance is a matrix. The inverse of the variance matrix is called the "information matrix".

The Durbin–Wu–Hausman test (also called Hausman specification test) is a statistical hypothesis test in econometrics named after James Durbin, De-Min Wu, and Jerry A. Hausman. The test evaluates the consistency of an estimator when compared to an alternative, less efficient estimator which is already known to be consistent. It helps one evaluate if a statistical model corresponds to the data.

Physical Review E The NSB estimator uses a mixture of Dirichlet prior, chosen such that the induced prior over the entropy is approximately uniform.

John Wiley. The Hodges–Lehmann estimator is much better than the sample mean when estimating mixtures of normal distributions, also.Jureckova Sen. Robust Statistical Procedures.

For large samples, the shrinkage intensity will reduce to zero, hence in this case the shrinkage estimator will be identical to the empirical estimator. Apart from increased efficiency the shrinkage estimate has the additional advantage that it is always positive definite and well conditioned. Various shrinkage targets have been proposed: # the identity matrix, scaled by the average sample variance; # the single-index model; # the constant-correlation model, where the sample variances are preserved, but all pairwise correlation coefficients are assumed to be equal to one another; # the two-parameter matrix, where all variances are identical, and all covariances are identical to one another (although not identical to the variances); # the diagonal matrix containing sample variances on the diagonal and zeros everywhere else; # the identity matrix. The shrinkage estimator can be generalized to a multi-target shrinkage estimator that utilizes several targets simultaneously.

The algorithm below chooses each vertex u to maximize the resulting pessimistic estimator. By the previous considerations, this keeps the pessimistic estimator from decreasing and guarantees a successful outcome. Below, N(t)(u) denotes the neighbors of u in R(t) (that is, neighbors of u that are neither in S nor have a neighbor in S). 1\. Initialize S to be the empty set. 2\.

There are two methods of doing this: balloon and pointwise estimation. In a balloon estimator, the kernel width is varied depending on the location of the test point. In a pointwise estimator, the kernel width is varied depending on the location of the sample. For multivariate estimators, the parameter, h, can be generalized to vary not just the size, but also the shape of the kernel.

Any minimum-variance mean-unbiased estimator minimizes the risk (expected loss) with respect to the squared-error loss function (among mean-unbiased estimators), as observed by Gauss. A minimum-average absolute deviation median-unbiased estimator minimizes the risk with respect to the absolute loss function (among median- unbiased estimators), as observed by Laplace. Other loss functions are used in statistics, particularly in robust statistics.

In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some “best possible” manner. The notion of “best possible” relies upon the choice of a particular loss function — the function which quantifies the relative degree of undesirability of estimation errors of different magnitudes. The most common choice of the loss function is quadratic, resulting in the mean squared error criterion of optimality.

The OLS estimator is consistent when the regressors are exogenous, and—by the Gauss–Markov theorem—optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated. Under these conditions, the method of OLS provides minimum- variance mean-unbiased estimation when the errors have finite variances. Under the additional assumption that the errors are normally distributed, OLS is the maximum likelihood estimator.

This estimator is asymptotically consistent, but not Fisher consistent for any n. Alternatively, take a sequence of Fisher consistent estimators Sn, then define Tn = Sn for n < n0, and Tn = Sn0 for all n ≥n0. This estimator is Fisher consistent for all n, but not asymptotically consistent. A concrete example of this construction would be estimating the population mean as X1 regardless of the sample size.

Several other age estimators have been described in the literature. 1) Weidner et al. (2014) describe an age estimator for DNA from blood that uses only three CpG sites of genes hardly affected by aging (cg25809905 in integrin, alpha 2b (ITGA2B); cg02228185 in aspartoacylase (ASPA) and cg17861230 in phosphodiesterase 4C, cAMP specific (PDE4C)). The age estimator by Weidener et al. (2014) applies only to blood. Even in blood this sparse estimator is far less accurate than Horvath's epigenetic clock (Horvath 2014) when applied to data generated by the Illumina 27K or 450K platforms. Horvath S (2014-02-18 16:34) Comparison with the epigenetic clock (2014). Reader Comment.

Wooldridge, J.M., Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass As in general two-step M-estimator problem, asymptotic variance of a generated regressor estimator is usually different from that of the estimator with all regressors observed. Yet, in some special cases, the asymptotic variances of the two estimators are identical. To give one such example, consider the setting in which the regression function is linear in parameter and unobserved regressor is a scalar. Denoting the coefficient of unobserved regressor by \delta if \delta=0 and E[\triangledown\gamma h(W,\gamma) U]=0 then the asymptotic variance is independent of whether observing the regressor.

In statistics, the Lehmann–Scheffé theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation. The theorem states that any estimator which is unbiased for a given unknown quantity and that depends on the data only through a complete, sufficient statistic is the unique best unbiased estimator of that quantity. The Lehmann–Scheffé theorem is named after Erich Leo Lehmann and Henry Scheffé, given their two early papers. If T is a complete sufficient statistic for θ and E(g(T)) = τ(θ) then g(T) is the uniformly minimum-variance unbiased estimator (UMVUE) of τ(θ).

Second, if a high breakdown initial fit is used for outlier detection, the follow-up analysis might inherit some of the inefficiencies of the initial estimator.

Use of linear-drift estimators such as the Hadamard variance could also be employed. A linear drift removal could be employed using a moment- based estimator.

In each case the sample statistic is a consistent estimator of the population value, and this provides an intuitive justification for this type of approach to estimation.

For a Gaussian distribution, this is the best unbiased estimator (i.e., one with the lowest MSE among all unbiased estimators), but not, say, for a uniform distribution.

Conversely, there could be objections to combining channel estimates of different users, since no user would want their channel estimate to deteriorate in order to improve the average network performance. The James–Stein estimator has also found use in fundamental quantum theory, where the estimator has been used to improve the theoretical bounds of the entropic uncertainty principle (a recent development of the Heisenberg uncertainty principle) for more than three measurements.

The Leonard–Merritt mass estimator is a formula for estimating the mass of a spherical stellar system using the apparent (angular) positions and proper motions of its component stars. The distance to the stellar system must also be known. Like the virial theorem, the Leonard–Merritt estimator yields correct results regardless of the degree of velocity anisotropy. Its statistical properties are superior to those of the virial theorem.

A more efficient estimator is given by instead taking the 7% trimmed range (the difference between the 7th and 93rd percentiles) and dividing by 3 (corresponding to 86% of the data falling within ±1.5 standard deviations of the mean in a normal distribution); this yields an estimator having about 65% efficiency. Analogous measures of location are given by the median, midhinge, and trimean (or statistics based on nearby points).

The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled). The definition of an MSE differs according to whether one is describing a predictor or an estimator.

In statistical theory, a U-statistic is a class of statistics that is especially important in estimation theory; the letter "U" stands for unbiased. In elementary statistics, U-statistics arise naturally in producing minimum- variance unbiased estimators. The theory of U-statistics allows a minimum- variance unbiased estimator to be derived from each unbiased estimator of an estimable parameter (alternatively, statistical functional) for large classes of probability distributions.Cox & Hinkley (1974),p.

As in the usual FE method, the estimator uses time-demeaned variables to remove unobserved effect. Therefore, FEIV estimator would be of limited use if variables of interest include time-invariant ones. The above discussion has parallel to the exogenous case of RE and FE models. In the exogenous case, RE assumes uncorrelatedness between explanatory variables and unobserved effect, and FE allows for arbitrary correlation between the two.

The square root of a pooled variance estimator is known as a pooled standard deviation (also known as combined standard deviation, composite standard deviation, or overall standard deviation).

While originally motivated by Markowitz portfolio selection, the linear shrinkage estimator he developed in collaboration with Olivier Ledoit has been widely adopted by other researchers in a variety of scientific fields such as cancer research, chemistry, civil engineering, climatology, electrical engineering, genetics, geology, neuroscience, psychology, speech recognition, etc. The common feature between these applications is that the dimension of the covariance matrix is not negligible with respect to the size of the sample. In this case the usual estimator, the sample covariance matrix, is inaccurate and ill-conditioned. By contrast, the Ledoit-Wolf estimator is more accurate and guaranteed to be well-conditioned, even in the difficult case where matrix dimension exceeds sample size.

For each random variable, the sample mean is a good estimator of the population mean, where a "good" estimator is defined as being efficient and unbiased. Of course the estimator will likely not be the true value of the population mean since different samples drawn from the same distribution will give different sample means and hence different estimates of the true mean. Thus the sample mean is a random variable, not a constant, and consequently has its own distribution. For a random sample of N observations on the jth random variable, the sample mean's distribution itself has mean equal to the population mean E(X_j) and variance equal to \sigma^2_j/N, where \sigma^2_j is the population variance.

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. That MSE is almost always strictly positive can be attributed to either randomness, or the fact that the estimator does not account for information that could produce a more accurate estimate. The MSE is a measure of the quality of an estimator—it is always non-negative, and values closer to zero are better.

In estimation theory and statistics, the Cramér–Rao bound (CRB) expresses a lower bound on the variance of unbiased estimators of a deterministic (fixed, though unknown) parameter, stating that the variance of any such estimator is at least as high as the inverse of the Fisher information. The result is named in honor of Harald Cramér and C. R. Rao, but has independently also been derived by Maurice Fréchet, Georges Darmois, as well as Alexander Aitken and Harold Silverstone. An unbiased estimator which achieves this lower bound is said to be (fully) efficient. Such a solution achieves the lowest possible mean squared error among all unbiased methods, and is therefore the minimum variance unbiased (MVU) estimator.

National Highway Traffic Safety Administration (NHTSA). BAC Estimator [computer program]. Springfield, VA: National Technical Information Service, 1992. A breathalyzer is a device for estimating BAC from a breath sample.

Whelan was a contracts administrator, planner and estimator for General Dynamics Corp. from 1961 to 1969. He was a deputy district attorney of San Diego from 1969 to 1989.

Any mean-unbiased estimator minimizes the risk (expected loss) with respect to the squared-error loss function, as observed by Gauss. A median-unbiased estimator minimizes the risk with respect to the absolute-deviation loss function, as observed by Laplace. Other loss functions are used in statistical theory, particularly in robust statistics. The theory of median-unbiased estimators was revived by George W. Brown in 1947: Further properties of median-unbiased estimators have been reported.

Relying on the sample drawn from these options will yield an unbiased estimator. However, the sample size is no longer fixed upfront. This leads to a more complicated formula for the standard error of the estimator, as well as issues with the optics of the study plan (since the power analysis and the cost estimations often relate to a specific sample size). A third possible solution is to use probability proportionate to size sampling.

The average of all the sample absolute deviations about the mean of size 3 that can be drawn from the population is 44/81, while the average of all the sample absolute deviations about the median is 4/9. Therefore, the absolute deviation is a biased estimator. However, this argument is based on the notion of mean-unbiasedness. Each measure of location has its own form of unbiasedness (see entry on biased estimator).

Colbeck was born in Myrtleford, Victoria, and was educated at Devonport Technical College. He was a building estimator and supervisor, managing director and proprietor of a building consultancy before entering politics. In his early years, Colbeck gained qualifications in Small Business Management; Technology (Building); and Carpentry and Joinery Trade and Proficiency. He was an apprentice carpenter and joiner between 1977–79; a trainee estimator and supervisor 1977–79; and manager 1979–84.

Yaakov Bar-Shalom (May 11, 1941) is a Tracking/Sensor Fusion researcher. His work is associated with MS-MTT (Multi-Sensor, Multi-Target Tracking) and IMM (interacting-multiple-model) estimator.

In these cases, the observed difference between the roll yield and the cost-of-carry is neither a good estimator for the cost-of-carry nor for the price bias.

Under certain conditions, the maximum score estimator can be weak consistent, but its asymptotic properties are very complicated. This issue mainly comes from the non-smoothness of the objective function.

A parametric model of survival may not be possible or desirable. In these situations, the most common method to model the survival function is the non- parametric Kaplan–Meier estimator.

Automated TMA methods involve computations executed by computers. This allows for the simultaneous tracking of multiple targets. There exist several automated TMA methods such as: Maximum Likelihood Estimator (MLE), etc.

Also required of a buyer is the ensuring that all materials comply with health and safety guidelines, and that the project estimator is fully briefed on the cost of materials.

"Estimator variables"that is, factors connected to the witness or to the circumstances surrounding their observation of an individual in an effort at identification can affect the reliability of identification.

38, 45–71. It is constructed similarly to Hill's estimator but uses a non-random "tuning parameter". A comparison of Hill-type and RE-type estimators can be found in Novak.

DESTINI Estimator was rolled out in 2014 to Sundt Construction and then commercially released in 2015. Presently, the company is headquartered in Santander Tower (formerly called Thanksgiving Tower) of Downtown Dallas.

CoCoE (Contact Conductance Estimator), a project founded to solve this problem and create a centralized database of contact conductance data and a computer program that uses it, was started in 2006.

The Wishart distribution is the sampling distribution of the maximum-likelihood estimator (MLE) of the covariance matrix of a multivariate normal distribution. A derivation of the MLE uses the spectral theorem.

It can be shown that the truncated mean of the middle 24% sample order statistics (i.e., truncate the sample by 38% at each end) produces an estimate for the population location parameter that is more efficient than using either the sample median or the full sample mean. However, due to the fat tails of the Cauchy distribution, the efficiency of the estimator decreases as more of the sample gets used in the estimate. Note that for the Cauchy distribution, neither the truncated mean, full sample mean or sample median represents a maximum likelihood estimator, nor are any as asymptotically efficient as the maximum likelihood estimator; however, the maximum likelihood estimate is more difficult to compute, leaving the truncated mean as a useful alternative.

Because the variance of the estimator of a parameter vector is a matrix, the problem of "minimizing the variance" is complicated. Using statistical theory, statisticians compress the information-matrix using real- valued summary statistics; being real-valued functions, these "information criteria" can be maximized. Traditionally, statisticians have evaluated estimators and designs by considering some summary statistic of the covariance matrix (of an unbiased estimator), usually with positive real values (like the determinant or matrix trace). Working with positive real numbers brings several advantages: If the estimator of a single parameter has a positive variance, then the variance and the Fisher information are both positive real numbers; hence they are members of the convex cone of nonnegative real numbers (whose nonzero members have reciprocals in this same cone).

The state estimator is an integral part of the overall monitoring and control systems for transmission networks. It is mainly aimed at providing a reliable estimate of the system voltages. This information from the state estimator flows to control centers and database servers across the network.Yih-Fang Huang; Werner, S.; Jing Huang; Kashyap, N.; Gupta, V., "State Estimation in Electric Power Grids: Meeting New Challenges Presented by the Requirements of the Future Grid," Signal Processing Magazine, IEEE , vol.

The attractiveness of different estimators can be judged by looking at their properties, such as unbiasedness, mean square error, consistency, asymptotic distribution, etc. The construction and comparison of estimators are the subjects of the estimation theory. In the context of decision theory, an estimator is a type of decision rule, and its performance may be evaluated through the use of loss functions. When the word "estimator" is used without a qualifier, it usually refers to point estimation.

In the biased estimator, by using the sample mean instead of the true mean, you are underestimating each xi − µ by x − µ. We know that the variance of a sum is the sum of the variances (for uncorrelated variables). So, to find the discrepancy between the biased estimator and the true variance, we just need to find the expected value of (x − µ)2. This is just the variance of the sample mean, which is σ2/n.

Because the MAD is a more robust estimator of scale than the sample variance or standard deviation, it works better with distributions without a mean or variance, such as the Cauchy distribution.

However, the clustering problem can be framed as estimating the parameters of the underlying class-based language model: it is possible to develop a consistent estimator for this model under mild assumptions.

For example, the MAD of a sample from a standard Cauchy distribution is an estimator of the population MAD, which in this case is 1, whereas the population variance does not exist.

This method is known as systems GMM. Note that the consistency and efficiency of the estimator depends on validity of the assumption that the errors can be decomposed as in equation (1).

These modes are: (1) Record; (2) Nominal Cruise; (3) Medium Slow Cruise; (4) Slow Cruise; (5) Orbital Ops; (6) Av; (7) ATE (Attitude Estimator) Calibration. These 7 maps cover all spacecraft telemetry modes.

This identify is useful in developing a Bayes estimator for multivariate Gaussian distributions. The identity also finds applications in random matrix theory by relating determinants of large matrices to determinants of smaller ones.

The generalized least squares (GLS), developed by Aitken, extends the Gauss–Markov theorem to the case where the error vector has a non-scalar covariance matrix. The Aitken estimator is also a BLUE.

For univariate distributions that are symmetric about one median, the Hodges–Lehmann estimator is a robust and highly efficient estimator of the population median. If data are represented by a statistical model specifying a particular family of probability distributions, then estimates of the median can be obtained by fitting that family of probability distributions to the data and calculating the theoretical median of the fitted distribution. Pareto interpolation is an application of this when the population is assumed to have a Pareto distribution.

The multi-fractional order estimator (MFOE)Bell, J. W., Simple Disambiguation Of Orthogonal Projection In Kalman’s filter Derivation, Proceedings of the International Conference on Radar Systems, Glasgow, UK. October, 2012.Bell, J. W., A Simple Kalman Filter Alternative: The Multi-Fractional Order Estimator, IET-RSN, Vol. 7, Issue 8, October 2013. is a straightforward, practical, and flexible alternative to the Kalman filter (KF)Kalman, R. E., A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, Vol. 82D, Mar. 1960.

The Nelson–Aalen estimator is a non-parametric estimator of the cumulative hazard rate function in case of censored data or incomplete data. It is used in survival theory, reliability engineering and life insurance to estimate the cumulative number of expected events. An "event" can be the failure of a non- repairable component, the death of a human being, or any occurrence for which the experimental unit remains in the "failed" state (e.g., death) from the point at which it changed on.

In fact, even if all estimates have astronomical absolute values for their errors, if the expected value of the error is zero, the estimator is unbiased. Also, an estimator's being biased does not preclude the error of an estimate from being zero in a particular instance. The ideal situation is to have an unbiased estimator with low variance, and also try to limit the number of samples where the error is extreme (that is, have few outliers). Yet unbiasedness is not essential.

The James–Stein estimator is a nonlinear estimator of the mean of Gaussian random vectors which can be shown to dominate, or outperform, the ordinary least squares technique with respect to a mean-square error loss function. Thus least squares estimation is not an admissible estimation procedure in this context. Some others of the standard estimates associated with the normal distribution are also inadmissible: for example, the sample estimate of the variance when the population mean and variance are unknown.

However, panel data methods, such as the fixed effects estimator or alternatively, the first-difference estimator can be used to control for it. If \mu_i is not correlated with any of the independent variables, ordinary least squares linear regression methods can be used to yield unbiased and consistent estimates of the regression parameters. However, because \mu_i is fixed over time, it will induce serial correlation in the error term of the regression. This means that more efficient estimation techniques are available.

The Allan variance can then be calculated using the estimators given, and for practical purposes the overlapping estimator should be used due to its superior use of data over the non-overlapping estimator. Other estimators such as total or Theo variance estimators could also be used if bias corrections is applied such that they provide Allan variance-compatible results. To form the classical plots, the Allan deviation (square root of Allan variance) is plotted in log–log format against the observation interval τ.

Robust measures of scale can be used as estimators of properties of the population, either for parameter estimation or as estimators of their own expected value. For example, robust estimators of scale are used to estimate the population variance or population standard deviation, generally by multiplying by a scale factor to make it an unbiased consistent estimator; see scale parameter: estimation. For example, dividing the IQR by 2 erf−1(1/2) (approximately 1.349), makes it an unbiased, consistent estimator for the population standard deviation if the data follow a normal distribution. In other situations, it makes more sense to think of a robust measure of scale as an estimator of its own expected value, interpreted as an alternative to the population variance or standard deviation as a measure of scale.

However, using values other than n improves the estimator in various ways. Four common values for the denominator are n, n − 1, n + 1, and n − 1.5: n is the simplest (population variance of the sample), n − 1 eliminates bias, n + 1 minimizes mean squared error for the normal distribution, and n − 1.5 mostly eliminates bias in unbiased estimation of standard deviation for the normal distribution. Firstly, if the omniscient mean is unknown (and is computed as the sample mean), then the sample variance is a biased estimator: it underestimates the variance by a factor of (n − 1) / n; correcting by this factor (dividing by n − 1 instead of n) is called Bessel's correction. The resulting estimator is unbiased, and is called the (corrected) sample variance or unbiased sample variance.

Ebersole was the son of Noah Ebersole, auto mechanic and Geraldine Kathryn McCormick, housewife. Marion was the daughter of Samuel J. Sherwood, estimator and Maybelle Elizabeth Lehay.Indiana Marriages, 1811-2007. Database with images. FamilySearch.

He emigrated from England in 1953, married Alice in 1971 and was an estimator for a number of construction firms. In 1989 he played a major role in the reconstruction of the Empress Hotel.

Commonly used civil estimating software programs include B2W, HCSS HeavyBid and SharpeSoft Estimator. There are also a variety of different tools used for the digitization of plans from engineers, such as Planswift or PrebuiltML X.

When prices are measured with noise the RV may not estimate the desired quantity. This problem motivated the development of a wide range of robust realized measures of volatility, such as the realized kernel estimator.

In statistical inference, there are several approaches to estimation theory that can be used to decide immediately what estimators should be used according to those approaches. For example, ideas from Bayesian inference would lead directly to Bayesian estimators. Similarly, the theory of classical statistical inference can sometimes lead to strong conclusions about what estimator should be used. However, the usefulness of these theories depends on having a fully prescribed statistical model and may also depend on having a relevant loss function to determine the estimator.

It is also known as the 1-median,The more general k-median problem asks for the location of k cluster centers minimizing the sum of distances from each sample point to its nearest center. spatial median, Euclidean minisum point, or Torricelli point. The geometric median is an important estimator of location in statistics, where it is also known as the L1 estimator. It is also a standard problem in facility location, where it models the problem of locating a facility to minimize the cost of transportation.

As an alternative, many methods have been suggested to improve the estimation of the covariance matrix. All of these approaches rely on the concept of shrinkage. This is implicit in Bayesian methods and in penalized maximum likelihood methods and explicit in the Stein-type shrinkage approach. A simple version of a shrinkage estimator of the covariance matrix is represented by the Ledoit- Wolf shrinkage estimatorO. Ledoit and M. Wolf (2004a) "A well-conditioned estimator for large-dimensional covariance matrices " Journal of Multivariate Analysis 88 (2): 365—411.

A Civil estimator is a construction professional who bids on civil projects that have gone to tender. Civil estimators typically have a background in civil engineering, construction project management, or construction supervision. Estimators are responsible for obtaining tenders, obtaining of material costs, calculation of tenders taking into consideration project management and overheads. The role of an estimator can be a very pressured one, and requires a great level of concentration, some of which will result in erratic office hours to ensure tender return dates can be achieved.

The bias of maximum-likelihood estimators can be substantial. Consider a case where n tickets numbered from 1 through to n are placed in a box and one is selected at random, giving a value X. If n is unknown, then the maximum-likelihood estimator of n is X, even though the expectation of X given n is only (n + 1)/2; we can be certain only that n is at least X and is probably more. In this case, the natural unbiased estimator is 2X − 1\.

Sampling distributions of two alternative estimators for a parameter β0. Although β1^ is unbiased, it is clearly inferior to the biased β2^. Ridge regression is one example of a technique where allowing a little bias may lead to a considerable reduction in variance, and more reliable estimates overall. While bias quantifies the average difference to be expected between an estimator and an underlying parameter, an estimator based on a finite sample can additionally be expected to differ from the parameter due to the randomness in the sample.

The maximum spacing estimator is a consistent estimator in that it converges in probability to the true value of the parameter, θ0, as the sample size increases to infinity. The consistency of maximum spacing estimation holds under much more general conditions than for maximum likelihood estimators. In particular, in cases where the underlying distribution is J-shaped, maximum likelihood will fail where MSE succeeds. An example of a J-shaped density is the Weibull distribution, specifically a shifted Weibull, with a shape parameter less than 1.

The significance of this choice is that this weighted mean is the maximum likelihood estimator of the mean of the probability distributions under the assumption that they are independent and normally distributed with the same mean.

More generally, an M-estimator may be defined to be a zero of an estimating function.Vidyadhar P. Godambe, editor. Estimating functions, volume 7 of Oxford Statistical Science Series. The Clarendon Press Oxford University Press, New York, 1991.

A study published in 2012 reported results of estimating above-ground biomass (AGB) and identifying low-intensity logging areas in the forest using airborne scanning lidar. Scans were made of two unlogged areas in the forest and one with low-intensity selective logging. A model-assisted estimator and synthetic estimator both gave accurate measures of the amount of biomass that had been removed, as confirmed by ground-based checks. Even when the residual canopy remained closed, the lidar could identify harvest areas, roads, skid trails and landings, and the reduction of biomass that had resulted.

As for the calculation of control limits, the standard deviation (error) required is that of the common-cause variation in the process. Hence, the usual estimator, in terms of sample variance, is not used as this estimates the total squared-error loss from both common- and special-causes of variation. An alternative method is to use the relationship between the range of a sample and its standard deviation derived by Leonard H. C. Tippett, as an estimator which tends to be less influenced by the extreme observations which typify special-causes.

This idea is complementary to overfitting and, separately, to the standard adjustment made in the coefficient of determination to compensate for the subjunctive effects of further sampling, like controlling for the potential of new explanatory terms improving the model by chance: that is, the adjustment formula itself provides "shrinkage." But the adjustment formula yields an artificial shrinkage. A shrinkage estimator is an estimator that, either explicitly or implicitly, incorporates the effects of shrinkage. In loose terms this means that a naive or raw estimate is improved by combining it with other information.

In some cases, the first-order conditions of the likelihood function can be solved explicitly; for instance, the ordinary least squares estimator maximizes the likelihood of the linear regression model. Under most circumstances, however, numerical methods will be necessary to find the maximum of the likelihood function. From the vantage point of Bayesian inference, MLE is a special case of maximum a posteriori estimation (MAP) that assumes a uniform prior distribution of the parameters. In frequentist inference, MLE is a special case of an extremum estimator, with the objective function being the likelihood.

In 2010, a College Affordability Estimator net price calculator was added to help prospective students estimate their individual net cost to attend a specific university. The Estimator meets the requirements of the Higher Education Opportunity Act. Institutions and systems can use the College Portraits to meet accountability requirements from governing boards, state legislatures, state coordinating offices, and other outside groups, often reducing their burden and duplication of effort. The College Portraits can also be used during the accreditation process as evidence of student learning outcomes, institutional improvement, transparency, and commitment to the public good.

In statistics, the concept of being an invariant estimator is a criterion that can be used to compare the properties of different estimators for the same quantity. It is a way of formalising the idea that an estimator should have certain intuitively appealing qualities. Strictly speaking, "invariant" would mean that the estimates themselves are unchanged when both the measurements and the parameters are transformed in a compatible way, but the meaning has been extended to allow the estimates to change in appropriate ways with such transformations.see section 5.2.

Estimators of market-beta have to wrestle with two important problems: # The underlying market betas are known to move over time. # Investors are interested in the best forecast of the true prevailing market-beta most indicative of the most likely future market-beta realization (which will be the realized risk contribution to their portfolios) and not in the historical market-beta. Despite these problems, a historical beta estimator remains an obvious benchmark predictor. It is obtained as the slope of the fitted line from the linear least-squares estimator.

One of the earliest attempts to analyse a statistical problem involving censored data was Daniel Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination. reprinted in Bradley (1971) 21 and Blower (2004) An early paper to use the Kaplan–Meier estimator for estimating censored costs was Quesenberry et al. (1989), however this approach was found to be invalid by Lin et al. unless all patients accumulated costs with a common deterministic rate function over time, they proposed an alternative estimation technique known as the Lin estimator.

In the comparison of various statistical procedures, efficiency is a measure of quality of an estimator, of an experimental design, or of a hypothesis testing procedure. Essentially, a more efficient estimator, experiment, or test needs fewer observations than a less efficient one to achieve a given performance. This article primarily deals with efficiency of estimators. The relative efficiency of two procedures is the ratio of their efficiencies, although often this concept is used where the comparison is made between a given procedure and a notional "best possible" procedure.

When analyzing experiments with varying probabilities of assignment, special precautions should be taken. These differences in assignment probabilities may be neutralized by inverse- probability-weighted (IPW) regression, where each observation is weighted by the inverse of its likelihood of being assigned to the treatment condition observed using the Horvitz-Thompson estimator. This approach addresses the bias that might arise if potential outcomes were systematically related to assignment probabilities. The downside of this estimator is that it may be fraught with sampling variability if some observations are accorded a high amount of weight (i.e.

To be more specific, the distribution of the estimator tn converges weakly to a dirac delta function centered at \theta. The central limit theorem implies asymptotic normality of the sample mean \bar X as an estimator of the true mean. More generally, maximum likelihood estimators are asymptotically normal under fairly weak regularity conditions — see the asymptotics section of the maximum likelihood article. However, not all estimators are asymptotically normal; the simplest examples are found when the true value of a parameter lies on the boundary of the allowable parameter region.

It can also be used to check the validity of extra instruments by comparing IV estimates using a full set of instruments Z to IV estimates that use a proper subset of Z. Note that in order for the test to work in the latter case, we must be certain of the validity of the subset of Z and that subset must have enough instruments to identify the parameters of the equation. Hausman also showed that the covariance between an efficient estimator and the difference of an efficient and inefficient estimator is zero.

The median of a sample is equivariant for a much larger group of transformations, the (strictly) monotonic functions of the real numbers. This analysis indicates that the median is more robust against certain kinds of changes to a data set, and that (unlike the mean) it is meaningful for ordinal data.. Revision of a chapter in Disseminations of the International Statistical Applications Institute (4th ed.), vol. 1, 1995, Wichita: ACG Press, pp. 61–66. The concepts of an invariant estimator and equivariant estimator have been used to formalize this style of analysis.

The reconstruction of a density field from a discrete set of points sampling this field.The Delaunay tessellation field estimator (DTFE), (or Delone tessellation field estimator (DTFE)) is a mathematical tool for reconstructing a volume-covering and continuous density or intensity field from a discrete point set. The DTFE has various astrophysical applications, such as the analysis of numerical simulations of cosmic structure formation, the mapping of the large-scale structure of the universe and improving computer simulation programs of cosmic structure formation. It has been developed by Willem Schaap and Rien van de Weijgaert.

A hungrier dog hunts even better. Law Number VII: Decreased business base increases overhead. So does increased business base. Law Number VIII: The most unsuccessful four years in the education of a cost-estimator is fifth grade arithmetic.

LIMDEP was first developed in the early 1980s. Econometric Software, Inc. was founded in 1985 by William H. Greene. The program was initially developed as an easy to use tobit estimator—hence the name, LIMited DEPendent variable models.

For instance, the 5% trimmed mean is obtained by taking the mean of the 5% to 95% range. In some cases a trimmed estimator discards a fixed number of points (such as maximum and minimum) instead of a percentage.

The two-sample Hodges–Lehmann estimator need not estimate the difference of two means or the difference of two (pseudo-)medians; rather, it estimates the differences between the population of the paired random–variables drawn respectively from the populations.

Consistency as defined here is sometimes referred to as weak consistency. When we replace convergence in probability with almost sure convergence, then the estimator is said to be strongly consistent. Consistency is related to bias; see bias versus consistency.

Furthermore, we may not know the survival status of all those who were vaccinated, so that assumptions will have to be made in this regard in order to define an estimator. One possible estimator for obtaining a specific estimate might be a hazard ratio based on a survival analysis that assumes a particular survival distribution conducted on all subjects to whom the intervention was offered, treating those who were lost to follow-up to be right-censored under random censorship. It might be that the trial population differs from the population, on which the vaccination campaign would be conducted, in which case this might also have to be taken into account. An alternative estimator used in a sensitivity analysis might assume that people, who were not followed for their vital status to the end of the trial, may be more likely to have died by a certain amount.

It was first proposed by F. Y. Edgeworth in 1888. Like the median, it is useful as an estimator of central tendency, robust against outliers. It allows for non-uniform statistical weights related to, e.g., varying precision measurements in the sample.

The truncated mean uses more information from the distribution or sample than the median, but unless the underlying distribution is symmetric, the truncated mean of a sample is unlikely to produce an unbiased estimator for either the mean or the median.

The winsorized mean uses more information from the distribution or sample than the median. However, unless the underlying distribution is symmetric, the winsorized mean of a sample is unlikely to produce an unbiased estimator for either the mean or the median.

Uses and modifications for the "moosehorn" crown closure estimator. Journal of Forestry 47(9):733:735. Other methods for estimating crown closure include the use of line-intercept, spherical densiometer, and hemispherical photography.Fiala, A.C.S.. Garman, S.L., and A.N. Gray. 2006.

In 1822, Gauss was able to state that the least-squares approach to regression analysis is optimal in the sense that in a linear model where the errors have a mean of zero, are uncorrelated, and have equal variances, the best linear unbiased estimator of the coefficients is the least-squares estimator. This result is known as the Gauss–Markov theorem. The idea of least-squares analysis was also independently formulated by the American Robert Adrain in 1808. In the next two centuries workers in the theory of errors and in statistics found many different ways of implementing least squares.

Since both the RCC and CLS are based upon relaxation of the real feasibility set Q, the form in which Q is defined affects its relaxed versions. This of course affects the quality of the RCC and CLS estimators. As a simple example consider the linear box constraints: : l \leq a^T x \leq u which can alternatively be written as : (a^T x - l)(a^T x - u) \leq 0. It turns out that the first representation results with an upper bound estimator for the second one, hence using it may dramatically decrease the quality of the calculated estimator.

Log–log plots are an alternative way of graphically examining the tail of a distribution using a random sample. Caution has to be exercised however as a log–log plot is necessary but insufficient evidence for a power law relationship, as many non power-law distributions will appear as straight lines on a log–log plot. This method consists of plotting the logarithm of an estimator of the probability that a particular number of the distribution occurs versus the logarithm of that particular number. Usually, this estimator is the proportion of times that the number occurs in the data set.

Secondly, the unbiased estimator does not minimize mean squared error (MSE), and generally has worse MSE than the uncorrected estimator (this varies with excess kurtosis). MSE can be minimized by using a different factor. The optimal value depends on excess kurtosis, as discussed in mean squared error: variance; for the normal distribution this is optimized by dividing by n + 1 (instead of n − 1 or n). Thirdly, Bessel's correction is only necessary when the population mean is unknown, and one is estimating both population mean and population variance from a given sample, using the sample mean to estimate the population mean.

Real-world observations such as the measurements of yesterday's rain throughout the day typically cannot be complete sets of all possible observations that could be made. As such, the variance calculated from the finite set will in general not match the variance that would have been calculated from the full population of possible observations. This means that one estimates the mean and variance that would have been calculated from an omniscient set of observations by using an estimator equation. The estimator is a function of the sample of n observations drawn without observational bias from the whole population of potential observations.

An estimator can be unbiased but not consistent. For example, for an iid sample {x,..., x} one can use T(X) = x as the estimator of the mean E[x]. Note that here the sampling distribution of T is the same as the underlying distribution (for any n, as it ignores all points but the last), so E[T(X)] = E[x] and it is unbiased, but it does not converge to any value. However, if a sequence of estimators is unbiased and converges to a value, then it is consistent, as it must converge to the correct value.

The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.

In statistical classification, the rule which assigns a class to a new data- item can be considered to be a special type of estimator. A number of invariance-type considerations can be brought to bear in formulating prior knowledge for pattern recognition.

An example of a Kaplan–Meier plot for two conditions associated with patient survival. The Kaplan–Meier estimator,Kaplan, E.L. in a retrospective on the seminal paper in "This week's citation classic". Current Contents 24, 14 (1983). Available from UPenn as PDF.

Anthony Thompson promised to manumit Tubman's father at the age of 45. After Thompson died, his son followed through with that promise in 1840. Tubman's father continued working as a timber estimator and foreman for the Thompson family.Clinton 2004, pp. 23–24.

Erich Leo Lehmann (20 November 1917 – 12 September 2009) was an American statistician, who made a major contribution to nonparametric hypothesis testing. He is one of the eponyms of the Lehmann–Scheffé theorem and of the Hodges–Lehmann estimator of the median of a population.

The ratio estimator given by this scheme is unbiased. Särndal, Swensson, and Wretman credit Lahiri, Midzuno and Sen for the insights leading to this methodSärndal, C-E, B Swensson J Wretman (1992) Model assisted survey sampling. Springer, §7.3.1 (iii) but Lahiri's technique is biased high.

Beck Technology is a software development company servicing the construction industry. The company is based in Dallas, Texas. Beck Technology offers a suite of products under DESTINI: design estimation integration initiative. Products include DESTINI Profiler (aka DProfiler), DESTINI Estimator, and DESTINI Optioneer (as a service).

The Heckman correction is a two-step M-estimator where the covariance matrix generated by OLS estimation of the second stage is inconsistent. Correct standard errors and other statistics can be generated from an asymptotic approximation or by resampling, such as through a bootstrap.

Art Young was laid down on 5 October 1944, under a Maritime Commission (MARCOM) contract, MC hull 2328, by J.A. Jones Construction, Panama City, Florida; sponsored by Mrs. J. Philo Caldwell, wife of the chief estimator at JAJCC, and launched on 13 November 1944.

He is a founding member of the Center for Computational Relativity and Gravitation at RIT. His scientific contributions include Osipkov–Merritt models, black hole spin flips, the Leonard–Merritt mass estimator, the M–sigma relation, stellar systems with negative temperatures, and the Schwarzschild Barrier.

Kaplan–Meier estimator in panel 6). Figure reproduced in part from and. After identification of the cell population of interest, a cross sample analysis can be performed to identify phenotypical or functional variations that are correlated with an external variable (e.g., a clinical outcome).

Subsampling is an alternative method for approximating the sampling distribution of an estimator. The two key differences to the bootstrap are: (i) the resample size is smaller than the sample size and (ii) resampling is done without replacement. The advantage of subsampling is that it is valid under much weaker conditions compared to the bootstrap. In particular, a set of sufficient conditions is that the rate of convergence of the estimator is known and that the limiting distribution is continuous; in addition, the resample (or subsample) size must tend to infinity together with the sample size but at a smaller rate, so that their ratio converges to zero.

A well-known example arises in the estimation of the population variance by sample variance. For a sample size of n, the use of a divisor n − 1 in the usual formula (Bessel's correction) gives an unbiased estimator, while other divisors have lower MSE, at the expense of bias. The optimal choice of divisor (weighting of shrinkage) depends on the excess kurtosis of the population, as discussed at mean squared error: variance, but one can always do better (in terms of MSE) than the unbiased estimator; for the normal distribution a divisor of n + 1 gives one which has the minimum mean squared error.

The resulting MPTs from each analysis are pooled, and the results are usually presented on a 50% Majority Rule Consensus tree, with individual branches (or nodes) labelled with the percentage of bootstrap MPTs in which they appear. This "bootstrap percentage" (which is not a P-value, as is sometimes claimed) is used as a measure of support. Technically, it is supposed to be a measure of repeatability, the probability that that branch (node, clade) would be recovered if the taxa were sampled again. Experimental tests with viral phylogenies suggest that the bootstrap percentage is not a good estimator of repeatability for phylogenetics, but it is a reasonable estimator of accuracy.

Anderson and Hsiao (1981) first proposed a solution by utilising instrumental variables (IV) estimation.. However, the Anderson–Hsiao estimator is asymptotically inefficient, as its asymptotic variance is higher than the Arellano–Bond estimator, which uses a similar set of instruments, but uses generalized method of moments estimation rather than instrumental variables estimation. In the Arellano–Bond method, first difference of the regression equation are taken to eliminate the individual effects. Then, deeper lags of the dependent variable are used as instruments for differenced lags of the dependent variable (which are endogenous). In traditional panel data techniques, adding deeper lags of the dependent variable reduces the number of observations available.

Simple L-estimators can be visually estimated from a box plot, and include interquartile range, midhinge, range, mid-range, and trimean. In statistics, an L-estimator is an estimator which is an L-statistic – a linear combination of order statistics of the measurements. This can be as little as a single point, as in the median (of an odd number of values), or as many as all points, as in the mean. The main benefits of L-estimators are that they are often extremely simple, and often robust statistics: assuming sorted data, they are very easy to calculate and interpret, and are often resistant to outliers.

For example, a single observation is itself an unbiased estimate of the mean and a pair of observations can be used to derive an unbiased estimate of the variance. The U-statistic based on this estimator is defined as the average (across all combinatorial selections of the given size from the full set of observations) of the basic estimator applied to the sub-samples. Sen (1992) provides a review of the paper by Wassily Hoeffding (1948), which introduced U-statistics and set out the theory relating to them, and in doing so Sen outlines the importance U-statistics have in statistical theory. Sen saysSen (1992) p.

In the example above, the algorithm was guided by the conditional expectation of a random variable F. In some cases, instead of an exact conditional expectation, an upper bound (or sometimes a lower bound) on some conditional expectation is used instead. This is called a pessimistic estimator.

Yet, there are cases in which the two estimators have the same asymptotic variance. One such case occurs if E[\triangledown\gamma h(W,\gamma)]=0[4]In this special case, inference on the estimated parameter can be conducted with the usual IV standard error estimator.

There are parametric (see Embrechts et al.) and non-parametric (see, e.g., Novak) approaches to the problem of the tail-index estimation. To estimate the tail-index using the parametric approach, some authors employ GEV distribution or Pareto distribution; they may apply the maximum-likelihood estimator (MLE).

Econometric Software, Inc. was founded in the early 1980s by William H. Greene. NLOGIT was released in 1996 with the development of the FIML nested logit estimator, originally an extension of the multinomial logit model in LIMDEP. The program derives its name from the Nested LOGIT model.

Margaret Wu (born June 28, 1950) is an Australian statistician and psychometrician who specialises in educational management. Wu helped to design the Watterson estimator which can be used to determine the genetic diversity of a population. She is an emeritus professor at the University of Melbourne.

This definition is based on the statistical expected value, integrating over infinite time. The real-world situation does not allow for such time-series, in which case a statistical estimator needs to be used in its place. A number of different estimators will be presented and discussed.

The response time is the amount of time a job spends in the system from the instant of arrival to the time they leave the system. A consistent and asymptotically normal estimator for the mean response time, can be computed as the fixed point of an empirical Laplace transform.

This choice can be related to choosing a statistical estimator for the quantity to be reconstructed. # Designing fast and robust algorithms that compute the solution to Step 2. These algorithms often use techniques from mathematical optimization and mapping such methods to fast computing platforms to build practical systems.

An estimand is a variable which is to be estimated in a statistical analysis. The term is used to more clearly distinguish the target of inference from the function to obtain this parameter (i.e., the estimator) and the specific value obtained from a given data set (i.e., the estimate).

Their specialty offering for consumer devices includes digital-to-analog converters for sound-processing and measurement and analog-to-digital converters for audio applications with their power regulators. Their general-purpose business is in Electronic Design Automation (EDA): mixed-signal simulator, schematics editor, and mixed-signal power consumption estimator.

The truncated mean is a useful estimator because it is less sensitive to outliers than the mean but will still give a reasonable estimate of central tendency or mean for many statistical models. In this regard it is referred to as a robust estimator. For example, in its use in Olympic judging, truncating the maximum and minimum prevents a single judge from increasing or lowering the overall score by giving an exceptionally high or low score. One situation in which it can be advantageous to use a truncated mean is when estimating the location parameter of a Cauchy distribution, a bell shaped probability distribution with (much) fatter tails than a normal distribution.

Under these assumptions an optimal control scheme within the class of linear control laws can be derived by a completion-of-squares argument. This control law which is known as the LQG controller, is unique and it is simply a combination of a Kalman filter (a linear–quadratic state estimator (LQE)) together with a linear–quadratic regulator (LQR). The separation principle states that the state estimator and the state feedback can be designed independently. LQG control applies to both linear time- invariant systems as well as linear time-varying systems, and constitutes a linear dynamic feedback control law that is easily computed and implemented: the LQG controller itself is a dynamic system like the system it controls.

Despite its drawbacks, in some cases it is useful: the midrange is a highly efficient estimator of μ, given a small sample of a sufficiently platykurtic distribution, but it is inefficient for mesokurtic distributions, such as the normal. For example, for a continuous uniform distribution with unknown maximum and minimum, the mid-range is the UMVU estimator for the mean. The sample maximum and sample minimum, together with sample size, are a sufficient statistic for the population maximum and minimum – the distribution of other samples, conditional on a given maximum and minimum, is just the uniform distribution between the maximum and minimum and thus add no information. See German tank problem for further discussion.

For example, the sample mean (estimator), denoted \overline X, can be used as an estimate of the mean parameter (estimand), denoted μ, of the population from which the sample was drawn. Similarly, the sample variance (estimator), denoted S2, can be used to estimate the variance parameter (estimand), denoted σ2, of the population from which the sample was drawn. (Note that the sample standard deviation (S) is not an unbiased estimate of the population standard deviation (σ): see Unbiased estimation of standard deviation.) It is possible to make statistical inferences without assuming a particular parametric family of probability distributions. In that case, one speaks of non-parametric statistics as opposed to the parametric statistics just described.

Despite the conceptual simplicity of the selection gradient, there are ongoing debates about its usefulness as an estimator of causes and consequences of natural selection. In 2017, Franklin & Morrissey showed that when performance measures such as body size, biomass, or growth rate are used in place of fitness components in regression-based analysis, accurate estimation of selection gradient is limited, which may lead to under- estimates of selection. Another complication of using selection gradient as an estimator of natural selection is when the phenotype of an individual is itself affected by individuals it interacts with. It complicates the process of separating direct and indirect selection as there are multiple ways selection can work.

In 1810, after reading Gauss's work, Pierre-Simon Laplace, after proving the central limit theorem, used it to give a large sample justification for the method of least squares and the normal distribution. In 1822, Gauss was able to state that the least-squares approach to regression analysis is optimal in the sense that in a linear model where the errors have a mean of zero, are uncorrelated, and have equal variances, the best linear unbiased estimator of the coefficients is the least-squares estimator. This result is known as the Gauss–Markov theorem. The publication in 1838 of Friedrich Wilhelm Bessel’s Gradmessung in Ostpreussen marked a new era in the science of geodesy.

In the summer of 1944 he joined an Operations analysis group and after some training served in that capacity (together with his fellow budding statisticians Erich Leo Lehmann and George Nicholson) with the Twentieth Air Force on Harmon Air Force Base, Guam. After the war he continued this work for another year in Washington, D.C. There he met Theodora Jane Long, and they married in 1947. He then joined the new statistics program at Berkeley and remained there for the rest of his career.Joe Hodges Memorial Hodges is best known for his contributions to the field of statistics, including the Hodges–Lehmann estimator, the nearest neighbor rule (with Evelyn Fix) and Hodges’ estimator.

But the sparse estimator was developed for pyrosequencing data and is highly cost effective. Wagner W (2014) Response to comment "comparison with the epigenetic clock by Horvath 2013" 2) Hannum et al. (2013) report several age estimators: one for each tissue type. Each of these estimators requires covariate information (e.g.

In statistics, Bayesian multivariate linear regression is a Bayesian approach to multivariate linear regression, i.e. linear regression where the predicted outcome is a vector of correlated random variables rather than a single scalar random variable. A more general treatment of this approach can be found in the article MMSE estimator.

Bienaymé had generalized the method of ordinary least squares. The dispute within the literature was over the superiority of one method over the other. It is now known that ordinary least squares is the best linear unbiased estimator, provided errors are uncorrelated and homoscedastic. At the time, this was not known.

Below it is shown how this estimator can be read as a coefficient in an ordinary least squares regression. The model described in this section is over-parametrized; to remedy that, one of the coefficients for the dummy variables can be set to 0, for example, we may set \gamma_1 = 0.

The trouble is that, without knowing θ, you don't know which of the n mean square errors are improved, so you can't use the Stein estimator only for those parameters. An example of the above setting occurs in channel estimation in telecommunications, for instance, because different factors affect overall channel performance.

Under heavy noise conditions, extracting the correlation coefficient between two sets of stochastic variables is nontrivial, in particular where Canonical Correlation Analysis reports degraded correlation values due to the heavy noise contributions. A generalization of the approach is given elsewhere. In case of missing data, Garren derived the maximum likelihood estimator.

According to Liang’s paper in 2010 (Liang, 2010), The smoothing spline technique was introduced in partially linear model by Engle, Heckman and Rice in 1986. After that, Robinson found an available LS estimator for nonparametric factors in partially linear model in 1988. At the same year, profile LS method was recommended by Speckman.

Edward Columbus Hosford was born in Eastman, Georgia, the son of Christopher Columbus Hosford and his wife, Hattie B. Pipkin Hosford. Little is known of his early life and education. His Dodge County draft registration card in 1918 shows that he was a "draftsman & estimator" for "Hugger Bros." [Construction Company] of "Brunswick, Ga".

The sample odds ratio n11n00 / n10n01 is easy to calculate, and for moderate and large samples performs well as an estimator of the population odds ratio. When one or more of the cells in the contingency table can have a small value, the sample odds ratio can be biased and exhibit high variance.

Motivation for post-estimate fusion is often consideration of uncertainty management. That is, the post-estimate fusion helps to narrow the uncertainty intervals of data-driven or model-based approaches. At the same time, the accuracy improves. The underlying notion is that multiple information sources can help to improve performance of an estimator.

In Julia, the CovarianceMatrices.jl package supports several types of heteroskedasticity and autocorrelation consistent covariance matrix estimation including Newey–West, White, and Arellano. In R, the packages `sandwich` and `plm` include a function for the Newey–West estimator. In Stata, the command `newey` produces Newey–West standard errors for coefficients estimated by OLS regression.

Getting a degree in computer-aided architectural engineering can qualify one for higher-level positions. This specialization is for students interested in having careers in architectural engineering and drafting.a CAAE can have jobs in many areas such as Expeditor, Construction Estimator, Project Manager, project architecture and many other fields related to these.

The figure presents an example of a performance-seeking control-flow diagram of the algorithm. The control law consists of estimation, modeling, and optimization processes. In the Kalman filter estimator, the inputs, outputs, and residuals were recorded. At the compact propulsion- system-modeling stage, all the estimated inlet and engine parameters were recorded.

This was usually carried out by a two person team comprising an assessor and an estimator. Assessors had no specific qualification other than to be seen as persons of good character with the ability to spot any unjustified or fraudulent claims. Retired police officers were often used. Estimators had building industry experience.

Paul Meier (July 24, 1924 – August 7, 2011) was a statistician who promoted the use of randomized trials in medicine. He is also known for introducing, with Edward L. Kaplan, the Kaplan–Meier estimator,Kaplan, E. L.; Meier, P.: Nonparametric estimation from incomplete observations. J. Amer. Statist. Assn. 53:457–481, 1958.

The simplest version of the minhash scheme uses different hash functions, where is a fixed integer parameter, and represents each set by the values of for these functions. To estimate using this version of the scheme, let be the number of hash functions for which , and use as the estimate. This estimate is the average of different 0-1 random variables, each of which is one when and zero otherwise, and each of which is an unbiased estimator of . Therefore, their average is also an unbiased estimator, and by standard deviation for sums of 0-1 random variables, its expected error is .. Therefore, for any constant there is a constant such that the expected error of the estimate is at most .

The concept of invariance is sometimes used on its own as a way of choosing between estimators, but this is not necessarily definitive. For example, a requirement of invariance may be incompatible with the requirement that the estimator be mean-unbiased; on the other hand, the criterion of median-unbiasedness is defined in terms of the estimator's sampling distribution and so is invariant under many transformations. One use of the concept of invariance is where a class or family of estimators is proposed and a particular formulation must be selected amongst these. One procedure is to impose relevant invariance properties and then to find the formulation within this class that has the best properties, leading to what is called the optimal invariant estimator.

Stein's example (or phenomenon or paradox), in decision theory and estimation theory, is the phenomenon that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average (that is, having lower expected mean squared error) than any method that handles the parameters separately. It is named after Charles Stein of Stanford University, who discovered the phenomenon in 1955. An intuitive explanation is that optimizing for the mean-squared error of a combined estimator is not the same as optimizing for the errors of separate estimators of the individual parameters. In practical terms, if the combined error is in fact of interest, then a combined estimator should be used, even if the underlying parameters are independent.

The outliers in the speed-of-light data have more than just an adverse effect on the mean; the usual estimate of scale is the standard deviation, and this quantity is even more badly affected by outliers because the squares of the deviations from the mean go into the calculation, so the outliers' effects are exacerbated. The plots below show the bootstrap distributions of the standard deviation, the median absolute deviation (MAD) and the Rousseeuw–Croux (Qn) estimator of scale. The plots are based on 10,000 bootstrap samples for each estimator, with some Gaussian noise added to the resampled data (smoothed bootstrap). Panel (a) shows the distribution of the standard deviation, (b) of the MAD and (c) of Qn. Image:speedOfLightScale.

While efficiency is a desirable quality of an estimator, it must be weighed against other considerations, and an estimator that is efficient for certain distributions may well be inefficient for other distributions. Most significantly, estimators that are efficient for clean data from a simple distribution, such as the normal distribution (which is symmetric, unimodal, and has thin tails) may not be robust to contamination by outliers, and may be inefficient for more complicated distributions. In robust statistics, more importance is placed on robustness and applicability to a wide variety of distributions, rather than efficiency on a single distribution. M-estimators are a general class of solutions motivated by these concerns, yielding both robustness and high relative efficiency, though possibly lower efficiency than traditional estimators for some cases.

Thus the mid-range, which is an unbiased and sufficient estimator of the population mean, is in fact the UMVU: using the sample mean just adds noise based on the uninformative distribution of points within this range. Conversely, for the normal distribution, the sample mean is the UMVU estimator of the mean. Thus for platykurtic distributions, which can often be thought of as between a uniform distribution and a normal distribution, the informativeness of the middle sample points versus the extrema values varies from "equal" for normal to "uninformative" for uniform, and for different distributions, one or the other (or some combination thereof) may be most efficient. A robust analog is the trimean, which averages the midhinge (25% trimmed mid-range) and median.

In practice, this generally happens. Firstly, while the sample variance (using Bessel's correction) is an unbiased estimator of the population variance, its square root, the sample standard deviation, is a biased estimate of the population standard deviation; because the square root is a concave function, the bias is downward, by Jensen's inequality. There is no general formula for an unbiased estimator of the population standard deviation, though there are correction factors for particular distributions, such as the normal; see unbiased estimation of standard deviation for details. An approximation for the exact correction factor for the normal distribution is given by using n − 1.5 in the formula: the bias decays quadratically (rather than linearly, as in the uncorrected form and Bessel's corrected form).

Discrete choice models are often estimated using maximum likelihood estimation. Logit models can be estimated by logistic regression, and probit models can be estimated by probit regression. Nonparametric methods, such as the maximum score estimator, have been proposed. Estimation of such models is usually done via parametric, semi- parametric and non-parametric maximum likelihood methods.

Isoline retrieval is a remote sensing inverse method that retrieves one or more isolines of a trace atmospheric constituent or variable. When used to validate another contour, it is the most accurate method possible for the task. When used to retrieve a whole field, it is a general, nonlinear inverse method and a robust estimator.

When considering how robust an estimator is to the presence of outliers, it is useful to test what happens when an extreme outlier is added to the dataset, and to test what happens when an extreme outlier replaces one of the existing datapoints, and then to consider the effect of multiple additions or replacements.

He retired from playing hockey following the 1935 to 1936 season with the Seattle Seahawks of the NWHL. His honors include being a member of the CHL Second All-Star Team in 1935. LaFrance later took a job as an electrician and estimator for the Universal Electric Company, in Duluth, Minnesota. He retired in 1969.

The Cramér–Rao bound is stated in this section for several increasingly general cases, beginning with the case in which the parameter is a scalar and its estimator is unbiased. All versions of the bound require certain regularity conditions, which hold for most well-behaved distributions. These conditions are listed later in this section.

Whether to use the bootstrap or the jackknife may depend more on operational aspects than on statistical concerns of a survey. The jackknife, originally used for bias reduction, is more of a specialized method and only estimates the variance of the point estimator. This can be enough for basic statistical inference (e.g., hypothesis testing, confidence intervals).

Since January 2005, Wymer has been counseling clients in nutrition, lifestyle changes and personal training. Wymer has two daughters, Lindsay and Madison, and has also worked as a construction estimator. In 2006, she became the first woman gymnast to be inducted into the University of Michigan Athletic Hall of Honor. Wymer has also published an informational pocket nutritional book.

Subsequently, Bhattacharya defined a cosine metric for distance between distributions, in a Calcutta Mathematical Society paper in 1943, expanding on some of the results in another paper in Sankhya in 1947. Bhattacharyya's two major research concerns were the measurement of divergence between two probability distributions and the setting of lower bounds to the variance of an unbiased estimator.

Each tree’s measurements are used to calculate the area projected by the crown onto the ground. Summing the crown areas for all trees measured on a fixed plot area and dividing by the ground area will give the crown closure. The "moosehorn" crown closure estimator is a device for measuring crown closure from the ground.Garrison, G.A. 1949.

An estimand is closely linked to the purpose or objective of an analysis. It describes what is to be estimated based on the question of interest. This is in contrast to an estimator, which defines the specific rule according to which the estimand is to be estimated. While the estimand will often be free of the specific assumptions e.g.

Quantity take-offs (QTO) are a detailed measurement of materials and labor needed to complete a construction project. They are developed by an estimator during the pre-construction phase. This process includes breaking the project down into smaller and more manageable units that are easier to measure or estimate. The level of detail required for measurement may vary.

The value of an equivariant map is often (imprecisely) called an invariant. In statistical inference, equivariance under statistical transformations of data is an important property of various estimation methods; see invariant estimator for details. In pure mathematics, equivariance is a central object of study in equivariant topology and its subtopics equivariant cohomology and equivariant stable homotopy theory.

By default, statistical packages report t-statistic with (these t-statistics are used to test the significance of corresponding regressor). However, when t-statistic is needed to test the hypothesis of the form , then a non-zero β0 may be used. If \scriptstyle\widehat\beta is an ordinary least squares estimator in the classical linear regression model (that is, with normally distributed and homoscedastic error terms), and if the true value of the parameter β is equal to β0, then the sampling distribution of the t-statistic is the Student's t-distribution with degrees of freedom, where n is the number of observations, and k is the number of regressors (including the intercept). In the majority of models, the estimator \scriptstyle\widehat\beta is consistent for β and is distributed asymptotically normally.

Learning curve showing training score and cross validation score In machine learning, a learning curve (or training curve) shows the validation and training score of an estimator for varying numbers of training samples. It is a tool to find out how much a machine learning model benefits from adding more training data and whether the estimator suffers more from a variance error or a bias error. If both the validation score and the training score converge to a value that is too low with increasing size of the training set, it will not benefit much from more training data. The machine learning curve is useful for many purposes including comparing different algorithms, choosing model parameters during design, adjusting optimization to improve convergence, and determining the amount of data used for training.

Whitney Kent Newey (born July 17, 1954) is the Jane Berkowitz Carlton and Dennis William Carlton Professor of Economics at the Massachusetts Institute of Technology and a well-known econometrician. He is best known for developing, with Kenneth D. West, the Newey–West estimator, which robustly estimates the covariance matrix of a regression model when errors are heteroskedastic and autocorrelated.

Balestra continued to be active in his retirement years. He taught at the University of Lugano until his death. Balestra his noted for his contributions to the econometrics of dynamic error components models, in particular for the generalized least squares estimator known as the Balestra–Nerlove estimator.See, for example, Balestra was one of the initiators of the foundation of the University of Lugano.

The rate of mutation within a population can be estimated using the Watterson estimator formula: θ=4Νeμ, where Νe is the effective population size and μ is the mutation rate (substitutions per site per unit of time). Hudson et al. proposed applying these variables to a chi- squared, goodness-of-fit test. The test statistic proposed by Hudson et al.

The time constants are sufficiently fast so that system dynamics decay away quickly (with respect to measurement frequency). The system appears to be progressing through a sequence of static states that are driven by various parameters like changes in load profile. The inputs of the state estimator can be given to various applications like Load Flow Analysis, Contingency Analysis, and other applications.

More generally, if the variance-covariance matrix of disturbance \epsilon_i across i has a nonconstant diagonal, the disturbance is heteroskedastic.Peter Kennedy, A Guide to Econometrics, 5th edition, p. 137. The matrices below are covariances when there are just three observations across time. The disturbance in matrix A is homoskedastic; this is the simple case where OLS is the best linear unbiased estimator.

This estimating function is often the derivative of another statistical function. For example, a maximum-likelihood estimate is the point where the derivative of the likelihood function with respect to the parameter is zero; thus, a maximum-likelihood estimator is a critical point of the score function. In many applications, such M-estimators can be thought of as estimating characteristics of the population.

This is because the all pole spectral model does not contain enough degree of freedom to match the know autocorrelation coefficients. Advantages and Disadvantages:- The advantage of this estimator is that errors in measuring or estimating the known autocorrelation coefficients can be taken into account since exact match is not required. The disadvantage is that too many computations are required.

NLOGIT is a full information maximum likelihood estimator for a variety of multinomial choice models. NLOGIT includes the discrete estimators in LIMDEP plus model extensions for multinomial logit (many specifications), random parameters mixed logit, random regret logit, WTP space specifications in mixed logit, scaled multinomial logit, nested logit, multinomial probit, heteroscedastic extreme value, error components, heteroscedastic logit and latent class models.

One of the main applications of the maximum entropy principle is in discrete and continuous density estimation. Similar to support vector machine estimators, the maximum entropy principle may require the solution to a quadratic programming and thus provide a sparse mixture model as the optimal density estimator. One important advantage of the method is able to incorporate prior information in the density estimation.

The estimate in this case is a single point in the parameter space. There also exists another type of estimator: interval estimators, where the estimates are subsets of the parameter space. The problem of density estimation arises in two applications. Firstly, in estimating the probability density functions of random variables and secondly in estimating the spectral density function of a time series.

After his discharge from the Air Force in July 1945, he attended UC Berkeley and majored in civil engineering. He graduated from UC Berkeley in 1950. In 1946, before completing his studies, he went to work for Gordon Ball Construction Company in Danville, California. He became an estimator for building bridges and highways until his death on May 25, 1967.

"Pennsylvania - Political Parties." Stats about All US Cities - Real Estate, Relocation Info, House Prices, Home Value Estimator, Recent Sales, Cost of Living, Crime, Race, Income, Photos, Education, Maps, Weather, Houses, Schools, Neighborhoods, and More. Web. 07 Sept. 2011. . In 1998, 42% of Pennsylvania's registered voters were Republican, 48% were Democrats, and the other 9% were either unaffiliated or with other parties.

The Akaike information criterion (AIC) is an estimator of the relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Thus, AIC provides a means for model selection. AIC was first formally described in a research paper by .

This technique is named after Friedrich Bessel. In estimating the population variance from a sample when the population mean is unknown, the uncorrected sample variance is the mean of the squares of deviations of sample values from the sample mean (i.e. using a multiplicative factor 1/n). In this case, the sample variance is a biased estimator of the population variance.

A biased rendering method is not necessarily wrong, and can still produce images close to those given by the rendering equation if the estimator is consistent. These methods, however, introduce a certain bias error (usually in the form of a blur) in efforts to reduce the variance (high-frequency noise). Often biased rendering is optimized to compute faster at the cost of accuracy.

The Kaplan–Meier estimator is one of the most frequently used methods of survival analysis. The estimate may be useful to examine recovery rates, the probability of death, and the effectiveness of treatment. It is limited in its ability to estimate survival adjusted for covariates; parametric survival models and the Cox proportional hazards model may be useful to estimate covariate-adjusted survival.

The unbiased estimation of standard deviation is a technically involved problem, though for the normal distribution using the term n − 1.5 yields an almost unbiased estimator. The unbiased sample variance is a U-statistic for the function ƒ(y1, y2) = (y1 − y2)2/2, meaning that it is obtained by averaging a 2-sample statistic over 2-element subsets of the population.

The bias and variance are both important measures of the quality of this estimator; efficiency is also often considered. A standard example of model selection is that of curve fitting, where, given a set of points and other background knowledge (e.g. points are a result of i.i.d. samples), we must select a curve that describes the function that generated the points.

In 2009, uShip entered a partnership with Ritchie Bros. Auctioneers, the world's largest auctioneer of heavy equipment, to provide real-time estimates and quotes for transportation of industrial equipment and vehicles being sold at auctions. In 2011, eBay Motors began incorporating uShip's Shipping Price Estimator as a vehicle shipping option within all its U.S. auto, motorcycle and power sports listings.

The common odds ratio estimator is denoted αMH and can be computed by the following equation: αMH = for all values of k and where Nk represents the total sample size at the kth interval. The obtained αMH is often standardized through log transformation, centering the value around 0.Dorans, N. J., & Holland, P. W. (1993). DIF detection and description: Mantel-Haenszel and standardization.

Selection algorithms still have the downside of requiring memory, that is, they need to have the full sample (or a linear- sized portion of it) in memory. Because this, as well as the linear time requirement, can be prohibitive, several estimation procedures for the median have been developed. A simple one is the median of three rule, which estimates the median as the median of a three-element subsample; this is commonly used as a subroutine in the quicksort sorting algorithm, which uses an estimate of its input's median. A more robust estimator is Tukey's ninther, which is the median of three rule applied with limited recursion: if is the sample laid out as an array, and :, then : The remedian is an estimator for the median that requires linear time but sub-linear memory, operating in a single pass over the sample.

When in under-sampled regime, having a prior on the distribution can help the estimation. One such Bayesian estimator was proposed in the neuroscience context known as the NSB (Nemenman–Shafee–Bialek) estimator.Ilya Nemenman, Fariel Shafee, William Bialek (2003) Entropy and Inference, Revisited. Advances in Neural Information ProcessingIlya Nemenman, William Bialek, de Ruyter (2004) Entropy and information in neural spike trains: Progress on the sampling problem.

Various software packages are available, such as javaPlex, Dionysus, Perseus, PHAT, DIPHA, GUDHI, Ripser, and TDAstats. A comparison between these tools is done by Otter et al. Giotto-tda is a Python package dedicated to integrating TDA in the machine learning workflow by means of a scikit-learn API. An R package TDA is capable of calculating recently invented concepts like landscape and the kernel distance estimator.

Results from studies are combined using different approaches. One approach frequently used in meta- analysis in health care research is termed 'inverse variance method'. The average effect size across all studies is computed as a weighted mean, whereby the weights are equal to the inverse variance of each study's effect estimator. Larger studies and studies with less random variation are given greater weight than smaller studies.

Journal of Forecasting, 34(7), 523-532. As a result, some scholars have utilized high frequency data to estimate half-life annual data. While use of high frequency data can face some limitations to discovering true half-life, mainly through the bias of an estimator, utilizing a high frequency ARMA model has been found to consistently and effectively estimate half-life with long annual data.

In statistics, the graphical lasso is a sparse penalized maximum likelihood estimator for the concentration or precision matrix (inverse of covariance matrix) of a multivariate elliptical distribution. The original variant was formulated to solve Dempster's covariance selection problem for the multivariate Gaussian distribution when observations were limited. Subsequently, the optimization algorithms to solve this problem were improved and extended to other types of estimators and distributions.

GUIDANCE is a web server used for estimating alignment confidence scores. RASER, the RAte Shift EstimatoR, is used to test site-specific evolutionary rate shifts. The Pepitope Server is used to map epitopes using affinity-selected peptides. Her work with autism genetic sequencing which won her the UNESCO-L’Oréal award, worked to identify where there were genetic variations that linked to individuals displaying autism.

T. Lancewicki and M. Aladjem (2014) "Multi-Target Shrinkage Estimation for Covariance Matrices", IEEE Transactions on Signal Processing, Volume: 62, Issue 24, pages: 6380-6390. Software for computing a covariance shrinkage estimator is available in R (packages corpcor and ShrinkCovMat), in Python (library scikit-learn), and in MATLAB.MATLAB code for shrinkage targets: scaled identity, single-index model, constant-correlation model, two-parameter matrix, and diagonal matrix.

Galaxy cluster MACS J2129-0741 and lensed galaxy MACS2129-1. Kaiser, Squires and Broadhurst (1995), Luppino & Kaiser (1997) and Hoekstra et al. (1998) prescribed a method to invert the effects of the Point Spread Function (PSF) smearing and shearing, recovering a shear estimator uncontaminated by the systematic distortion of the PSF. This method (KSB+) is the most widely used method in weak lensing shear measurements.

Typical (single-replica) MTD simulations can include up to 3 CVs, even using the multi-replica approach, it is hard to exceed 8 CVs, in practice. This limitation comes from the bias potential, constructed by adding Gaussian functions (kernels). It is a special case of the kernel density estimator (KDE). The number of required kernels, for a constant KDE accuracy, increases exponentially with the number of dimensions.

Construction cost estimating software is computer software designed for contractors to estimate construction costs for a specific project. A cost estimator will typically use estimating software to estimate their bid price for a project, which will ultimately become part of a resulting construction contract. Some architects, engineers, construction managers, and others may also use cost estimating software to prepare cost estimates for purposes other than bidding.

The kurtosis goes to infinity for high and low values of p, but for p=1/2 the two- point distributions including the Bernoulli distribution have a lower excess kurtosis than any other probability distribution, namely −2. The Bernoulli distributions for 0 \le p \le 1 form an exponential family. The maximum likelihood estimator of p based on a random sample is the sample mean.

An "estimator" or "point estimate" is a statistic (that is, a function of the data) that is used to infer the value of an unknown parameter in a statistical model. The parameter being estimated is sometimes called the estimand. It can be either finite-dimensional (in parametric and semi-parametric models), or infinite-dimensional (semi-parametric and non-parametric models).Kosorok (2008), Section 3.1, pp 35–39.

It has been used to estimate the differences between the members of two populations. It has been generalized from univariate populations to multivariate populations, which produce samples of vectors. It is based on the Wilcoxon signed-rank statistic. In statistical theory, it was an early example of a rank-based estimator, an important class of estimators both in nonparametric statistics and in robust statistics.

In the simplest case, the "Hodges–Lehmann" statistic estimates the location parameter for a univariate population.Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. Entry for "Hodges-Lehmann one-samaple estimator"Hodges & Lehmann (1963) Its computation can be described quickly. For a dataset with n measurements, the set of all possible one- or two-element subsets of it has n(n + 1)/2 elements.

A relatively simple situation is estimation of a proportion. For example, we may wish to estimate the proportion of residents in a community who are at least 65 years old. The estimator of a proportion is \hat p = X/n, where X is the number of 'positive' observations (e.g. the number of people out of the n sampled people who are at least 65 years old).

Chen graduated from the PLA Institute of Logistics Engineering, majoring in architecture. He had two years of experience working in the military between 1968 and 1970 as part of the PLA 6716 Squadron. From September 1970 to March 1983, Chen worked at the Shanghai Pengpu Machinery Factory as a worker and estimator. He was eventually promoted to the capital construction branch vice- section chief.

Layers of the neural network. R, G are weights used by the wake-sleep algorithm to modify data inside the layers. The wake-sleep algorithm is an unsupervised learning algorithm for a stochastic multilayer neural network. The algorithm adjusts the parameters so as to produce a good density estimator. There are two learning phases, the “wake” phase and the “sleep” phase, which are performed alternately.

The three- stage least squares estimator was introduced by . It can be seen as a special case of multi-equation GMM where the set of instrumental variables is common to all equations. If all regressors are in fact predetermined, then 3SLS reduces to seemingly unrelated regressions (SUR). Thus it may also be seen as a combination of two-stage least squares (2SLS) with SUR.

In P. W. Holland & H. Wainer (Eds.), Differential item functioning (pp. 35–66). Hillsdale, NJ: Erlbaum. The new transformed estimator MHD-DIF is computed as follows: MHD-DIF = -2.35ln(αMH) Thus an obtained value of 0 would indicate no DIF. In examining the equation, it is important to note that the minus sign changes the interpretation of values less than or greater than 0.

According to an interview with Jim Rough, former representative of the American Evaluation Association, in the magazine D+C Development and Cooperation, this method does not work for complex, multilayer matters. The single difference estimator compares mean outcomes at end-line and is valid where treatment and control groups have the same outcome values at baseline. The difference-in-difference (or double difference) estimator calculates the difference in the change in the outcome over time for treatment and comparison groups, thus utilizing data collected at baseline for both groups and a second round of data collected at end-line, after implementation of the intervention, which may be years later. Impact Evaluations which have to compare average outcomes in the treatment group, irrespective of beneficiary participation (also referred to as 'compliance' or 'adherence'), to outcomes in the comparison group are referred to as intention-to-treat (ITT) analyses.

Sieve estimators have been used extensively for estimating density functions in high-dimensional spaces such as in Positron emission tomography(PET). The first exploitation of Sieves in PET for solving the maximum-likelihood Positron emission tomography#Image reconstruction problem was by Donald Snyder and Michael Miller, where they stabilized the time-of-flight PET problem originally solved by Shepp and Vardi. Shepp and Vardi's introduction of Maximum-likelihood estimators in emission tomography exploited the use of the Expectation-Maximization algorithm, which as it ascended towards the maximum-likelihood estimator developed a series of artifacts associated to the fact that the underlying emission density was of too high a dimension for any fixed sample size of Poisson measured counts. Grenander's method of sieves was used to stabilize the estimator, so that for any fixed sample size a resolution could be set which was consistent for the number of counts.

A practical application of this occurs for example for random walks, since the probability for the time of the last visit to the origin in a random walk is distributed as the arcsine distribution Beta(1/2, 1/2): the mean of a number of realizations of a random walk is a much more robust estimator than the median (which is an inappropriate sample measure estimate in this case).

In population genetics, the Watterson estimator is a method for describing the genetic diversity in a population. It was developed by Margaret Wu and G. A. Watterson in the 1970s. It is estimated by counting the number of polymorphic sites. It is a measure of the "population mutation rate" (the product of the effective population size and the neutral mutation rate) from the observed nucleotide diversity of a population.

Ben Carré was born in Paris, France in 1883. His father, a professional painter and decorator, died when Carré was six-years-old. At thirteen, Carré left school to become an apprentice house-painting estimator. Finding his talent lay in painting rather than arithmetic, he took a job as an assistant scene painter at Atelier Amable, at the time one of the most important scenic art studios in Paris.

Because the ratio estimate is generally skewed confidence intervals created with the variance and symmetrical tests such as the t test are incorrect. These confidence intervals tend to overestimate the size of the left confidence interval and underestimate the size of the right. If the ratio estimator is unimodal (which is frequently the case) then a conservative estimate of the 95% confidence intervals can be made with the Vysochanskiï–Petunin inequality.

Cauchy developed the Cauchy distribution to show a case where the method of ordinary least squares resulted in a perfectly inefficient estimator. This is due to the fact that the Cauchy distribution has no defined variance to minimize. This is the first direct appearance of the Cauchy distribution in the academic literature. The curve had been previously studied by others, though in the English language as the Witch of Agnesi.

Barco ColorTone adds an "Image quality estimator" module (evaluate if an image is printable according to certain quality parameters), but lacks several of the other Creator modules. Using the "Brix Organizer" software it was possible to group CT-Brix modules into "sessions" customised for the current workflow. One could for example disable both colour correction and the creative functions/filters, giving the operator an interface more focused on painting.

They also form the background for parameter estimation. In the case of extremum estimators for parametric models, a certain objective function is maximized or minimized over the parameter space. Theorems of existence and consistency of such estimators require some assumptions about the topology of the parameter space. For instance, compactness of the parameter space, together with continuity of the objective function, suffices for the existence of an extremum estimator.

Clearblue Advanced Digital Pregnancy Test with Weeks Estimator In 1989, Clearblue released the first one-step home ovulation test, enabling women to measure their surge in Luteinising Hormone (LH) to determine their most fertile days. In 1999, the brand launched the world’s first dual-hormone fertility monitor, which allowed women to measure estrone3-glucuronide (estrogen) in combination with LH. The company created the first digital ovulation test in 2004.

In statistics, M-estimators are a broad class of extremum estimators for which the objective function is a sample average. Both non-linear least squares and maximum likelihood estimation are special cases of M-estimators. The definition of M-estimators was motivated by robust statistics, which contributed new types of M-estimators. The statistical procedure of evaluating an M-estimator on a data set is called M-estimation.

"A feasible Bayesian estimator of quantiles for projectile accuracy from non-i.i.d. data." Journal of the American Statistical Association, vol. 87 (419), pp. 676–681. Further, a well-known measure of accuracy for a group of projectiles is the circular error probable (CEP), which is the number R such that, on average, half of the group of projectiles falls within the circle of radius R about the target point.

Wu studied statistics at the University of Melbourne and graduated in 1972. She worked at Monash University as a research assistant from 1973 to 1988, where she taught herself to program. She worked with Watterson on the Watterson estimator, a means to determine the genetic diversity of a population. Despite her contributions to high-impact publications, Wu was never named as an author, and was not encouraged to complete a PhD.

The Gauss–Markov theorem states that regression models which fulfill the classical linear regression model assumptions provide the most efficient, linear and unbiased estimators. In ordinary least squares, the relevant assumption of the classical linear regression model is that the error term is uncorrelated with the regressors. The presence of omitted-variable bias violates this particular assumption. The violation causes the OLS estimator to be biased and inconsistent.

Pp. 123–130. compares the impacts of gymnasiums constructed of different building materials over a 200-year period using the Athena Impact Estimator. Rich developed the phrase "First Impacts" to describe the environmental impacts of new construction from raw material extraction to occupancy of the building. When the environmental impacts of maintenance and replacement are considered with first impacts for a building, a complete picture of the environmental impacts are formed.

The basic idea behind this type of convergence is that the probability of an “unusual” outcome becomes smaller and smaller as the sequence progresses. The concept of convergence in probability is used very often in statistics. For example, an estimator is called consistent if it converges in probability to the quantity being estimated. Convergence in probability is also the type of convergence established by the weak law of large numbers.

The midpoint of the distribution (a + b) / 2 is both the mean and the median of the uniform distribution. Although both the sample mean and the sample median are unbiased estimators of the midpoint, neither is as efficient as the sample mid-range, i.e. the arithmetic mean of the sample maximum and the sample minimum, which is the UMVU estimator of the midpoint (and also the maximum likelihood estimate).

Herbert Sichel (1915–1995) was a statistician who made great advances in the areas of both theoretical and applied statistics. He developed the Sichel-t estimator for the log-normal distribution's t-statistic. He also made great leaps in the area of the generalized inverse Gaussian distribution which became known as the Sichel distribution. Dr Sichel pioneered the science of geostatistics with Danie Krige in the early 1950s.

In an influential article in 1978, Wells proposed a distinction between two different types of variables influencing the accuracy of eyewitness identification (Wells, 1978). System-variables are variables that are (or could be) under the control of the justice system (e.g., pre-lineup instructions to witnesses). Estimator-variables are variables that are not under the control of the justice system, but are circumstantial factors that influence identification (e.g.

It covers the effective use of data, confidence intervals, effective degree of freedom, likewise introducing the overlapping Allan variance estimator. It is a highly recommended reading for those topics. The IEEE standard 1139 Standard definitions of Physical Quantities for Fundamental Frequency and Time Metrology is beyond that of a standard a comprehensive reference and educational resource. A modern book aimed towards telecommunication is Stefano Bregni "Synchronisation of Digital Telecommunication Networks".

For an unbiased estimator, the average of the signed deviations across the entire set of all observations from the unobserved population parameter value averages zero over an arbitrarily large number of samples. However, by construction the average of signed deviations of values from the sample mean value is always zero, though the average signed deviation from another measure of central tendency, such as the sample median, need not be zero.

In 2017, researchers successfully sequenced the full mtDNA genome from the femur. The results confirmed that the femur belonged to a Neanderthal. The mtDNA from the Hohlenstein-Stadel sample is highly divergent from those of other available Neanderthal samples. The addition of this mtDNA sample itself results in a near doubling of the genetic diversity of available Neanderthal mtDNA using Watterson's estimator theta; this suggests that Neanderthal mtDNA diversity was higher than previously presumed.

The species discovery curve can also be used. This curve relates the number of species found in an area as a function of the time. These curves can also be created by using estimators (such as the Good–Toulmin estimator) and plotting the number of unseen species at each value for t. A species discovery curve is always increasing, as there is never a sample that could decrease the number of discovered species.

Least trimmed squares (LTS) is a viable alternative and is currently (2007) the preferred choice of Rousseeuw and Ryan (1997, 2008). The Theil–Sen estimator has a lower breakdown point than LTS but is statistically efficient and popular. Another proposed solution was S-estimation. This method finds a line (plane or hyperplane) that minimizes a robust estimate of the scale (from which the method gets the S in its name) of the residuals.

In 1952 Midzuno and Sen independently described a sampling scheme that provides an unbiased estimator of the ratio.Midzuno H (1952) On the sampling system with probability proportional to the sum of the sizes. Ann Inst Stat Math 3: 99-107Sen AR (1952) Present status of probability sampling and its use in the estimation of a characteristic. Econometrika 20-103 The first sample is chosen with probability proportional to the size of the x variate.

If a linear relationship between the x and y variates exists and the regression equation passes through the origin then the estimated variance of the regression equation is always less than that of the ratio estimator. The precise relationship between the variances depends on the linearity of the relationship between the x and y variates: when the relationship is other than linear the ratio estimate may have a lower variance than that estimated by regression.

Example of a violin plot Example of a violin plot in a scientific publication in PLOS Pathogens. A violin plot is a method of plotting numeric data. It is similar to a box plot, with the addition of a rotated kernel density plot on each side. Violin plots are similar to box plots, except that they also show the probability density of the data at different values, usually smoothed by a kernel density estimator.

Ulf Grenander (23 July 1923 – 12 May 2016) was a Swedish statistician and professor of applied mathematics at Brown University. His early research was in probability theory, stochastic processes, time series analysis, and statistical theory (particularly the order-constrained estimation of cumulative distribution functions using his sieve estimator). In recent decades, Grenander contributed to computational statistics, image processing, pattern recognition, and artificial intelligence. He coined the term pattern theory to distinguish from pattern recognition.

The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective. The method approximates the optimal importance sampling estimator by repeating two phases:Rubinstein, R.Y. and Kroese, D.P. (2004), The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation, and Machine Learning, Springer-Verlag, New York . #Draw a sample from a probability distribution.

There are various definitions of a "robust statistic." Strictly speaking, a robust statistic is resistant to errors in the results, produced by deviations from assumptions, page 1. (e.g., of normality). This means that if the assumptions are only approximately met, the robust estimator will still have a reasonable efficiency, and reasonably small bias, as well as being asymptotically unbiased, meaning having a bias tending towards 0 as the sample size tends towards infinity.

For example, in estimating SUR model of 6 equations with 5 explanatory variables in each equation by Maximum Likelihood, the number of parameters declines from 51 to 30. Despite its appealing feature in computation, concentrating parameters is of limited use in deriving asymptotic properties of M-estimator. The presence of W in each summand of the objective function makes it difficult to apply the law of large numbers and the central limit theorem.

Equivalently, a Hadamard matrix has maximal determinant among matrices with entries of absolute value less than or equal to 1 and so is an extremal solution of Hadamard's maximal determinant problem. Certain Hadamard matrices can almost directly be used as an error-correcting code using a Hadamard code (generalized in Reed–Muller codes), and are also used in balanced repeated replication (BRR), used by statisticians to estimate the variance of a parameter estimator.

The Akaike information criterion (AIC) is an estimator of in-sample prediction error and thereby relative quality of statistical models for a given set of data. In-sample prediction error is the expected error in predicting the resampled response to a training sample. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Thus, AIC provides a means for model selection.

Hammond worked for several months after receiving his degree for the Kenwood Bridge Co. in Chicago. In 1908, he became associated with the Pressed Steel Car Co. of Pittsburgh. He worked for the latter company as a draftsman, estimator and sales agent at least into the 1920s. At the time of the 1910 United States Census, he was living in Chicago with his parents and working as a sales agent for a steel car company.

Random sampling by using lots is an old idea, mentioned several times in the Bible. In 1786 Pierre Simon Laplace estimated the population of France by using a sample, along with ratio estimator. He also computed probabilistic estimates of the error. These were not expressed as modern confidence intervals but as the sample size that would be needed to achieve a particular upper bound on the sampling error with probability 1000/1001.

Dorota Maria Dabrowska is a Polish statistician known for applying nonparametric statistics and semiparametric models to counting processes and survival analysis. Dabrowska's estimator, from her paper "Kaplan–Meier estimate on the plane" (Annals of Statistics, 1988) is a widely used tool for bivariate survival under random censoring. Dabrowska earned a master's degree in mathematics from the University of Warsaw. She completed her Ph.D. in statistics in 1984 at the University of California, Berkeley.

In the meantime, Pender had settled in a North Side Chicago neighborhood where she went under the name Ashley Thompson. She found a job as an estimator for a contractor.Escaped killer tells Fox 59 about life on the run Fox 59 WXIN, November 10, 2009. On December 22, 2008, two hours after a rerun of America's Most Wanted, her neighbor identified her and called the Chicago police, who arrested her at her apartment.

For nearly a decade before taking office, he worked as a senior property claims estimator for State Farm Insurance. A Republican, Losquadro won election to Suffolk County’s 6th Legislative District in November 2003 and served full- time until January 2011. He has served as chairman of the Environment, Planning and Agriculture Committee as well as the Veterans & Seniors Committee. In 2006, Losquadro was elected by his peers as the legislature’s Minority Leader.

Variational Bayesian learning is based on probabilities. There is a chance that an approximation is performed with mistakes, damaging further data representations. Another downside pertains to complicated or corrupted data samples, making it difficult to infer a representational pattern. The wake-sleep algorithm has been suggested not to be powerful enough for the layers of the inference network in order to recover a good estimator of the posterior distribution of latent variables.

Between 1984 and 1989 he was a building estimator and supervisor; and managing director and proprietor of building consultancy from 1989. From 1993–1996, and from 1998–2000, Colbeck served as the president of the Devonport Chamber of Commerce. From 1998–2001, he was a member of the Board of Directors of the Tasmanian Chamber of Commerce and Industry (TCCI). From 1999–2002, he was an Alderman of the Devonport City Council.

Ordinary least squares regression of Okun's law. Since the regression line does not miss any of the points by very much, the R2 of the regression is relatively high. Comparison of the Theil–Sen estimator (black) and simple linear regression (blue) for a set of points with outliers. Because of the many outliers, neither of the regression lines fits the data well, as measured by the fact that neither gives a very high R2.

When investigating the stability of crystal oscillators and atomic clocks, it was found that they did not have a phase noise consisting only of white noise, but also of flicker frequency noise. These noise forms become a challenge for traditional statistical tools such as standard deviation, as the estimator will not converge. The noise is thus said to be divergent. Early efforts in analysing the stability included both theoretical analysis and practical measurements.

In statistics, the jackknife is a resampling technique especially useful for variance and bias estimation. The jackknife pre-dates other common resampling methods such as the bootstrap. The jackknife estimator of a parameter is found by systematically leaving out each observation from a dataset and calculating the estimate and then finding the average of these calculations. Given a sample of size n, the jackknife estimate is found by aggregating the estimates of each (n-1)-sized sub-sample.

Taken this consideration, Halphen found the harmonic density function. Nowadays known as a hyperbolic distribution, has been studied by Rukhin (1974) and Barndorff- Nielsen (1978). The harmonic law is the only one two-parameter family of distributions that is closed under change of scale and under reciprocals, such that the maximum likelihood estimator of the population mean is the sample mean (Gauss' principle). In 1946, Halphen realized that introducing an additional parameter, flexibility could be improved.

Trimmed estimators can also be used as statistics in their own right – for example, the median is a measure of location, and the IQR is a measure of dispersion. In these cases, the sample statistics can act as estimators of their own expected value. For example, the MAD of a sample from a standard Cauchy distribution is an estimator of the population MAD, which in this case is 1, whereas the population variance does not exist.

Other recent work has focused more on the large sample properties of an estimator of the marginal mean treatment effect conditional on a treatment level in the context of a difference-in-differences model,Abadie, A. (2005): Semiparametric Difference-in-Differences Estimators. Review of Economic Studies 72(1), pp. 1–19. and on the efficient estimation of multi-valued treatment effects in a semiparametric framework.Cattaneo, M. D. (2010): Efficient Semiparametric Estimation of Multi-Valued Treatment Effects under Ignorability.

He is deeply involved in the economic development of the region of Portneuf. From 1993 to 1996, he was president and shareholder of Construction du Grand Portneuf. He was a project estimator and manager for the Joseph Linteau & Sons company (1992–1993) and also a manager for Magasin Rona in Saint-Raymond-de-Portneuf (1986–1992). He worked as a designer for the architectural firm Beaudet, Nolet & Arcam Inc, and also for VariaHab which specializes in prefabricated houses.

Speaking of an expectation (E) step is a bit of a misnomer. What are calculated in the first step are the fixed, data- dependent parameters of the function Q. Once the parameters of Q are known, it is fully determined and is maximized in the second (M) step of an EM algorithm. Although an EM iteration does increase the observed data (i.e., marginal) likelihood function, no guarantee exists that the sequence converges to a maximum likelihood estimator.

Further, Krichevskii became a doctor of physical and mathematical sciences (1988) and professor (1991), specializing in the field of mathematical cybernetics and information theory. From 1962 to 1996 he worked at the Sobolev Institute of Mathematics. In the late 90s he worked in University of California, Riverside, US. His main publications are in the fields of universal source coding, optimal hashing, combinatorial retrieval and error-correcting codes. Krichevsky–Trofimov estimator is widely used in source coding and bioinformatics.

The efficiencies and the relative efficiency of two procedures theoretically depend on the sample size available for the given procedure, but it is often possible to use the asymptotic relative efficiency (defined as the limit of the relative efficiencies as the sample size grows) as the principal comparison measure. An efficient estimator is characterized by a small variance or mean square error, indicating that there is a small deviance between the estimated value and the "true" value.

In this type of estimation, we select the multidimensional signal to be a separable function. Because of this property we will be able to view the Fourier analysis taking place in multiple dimensions successively. A time delay in the magnitude squaring operation will help us process the Fourier transformation in each dimension. A Discrete time Multidimensional Fourier transform is applied along each dimension and in the end a maximum entropy estimator is applied and the magnitude is squared.

Responses to nonzero autocorrelation include generalized least squares and the Newey–West HAC estimator (Heteroskedasticity and Autocorrelation Consistent). In the estimation of a moving average model (MA), the autocorrelation function is used to determine the appropriate number of lagged error terms to be included. This is based on the fact that for an MA process of order q, we have R(\tau) eq 0, for \tau = 0,1, \ldots , q, and R(\tau) = 0, for \tau >q.

When the observations are independent, this estimator has a (scaled) binomial distribution (and is also the sample mean of data from a Bernoulli distribution). The maximum variance of this distribution is 0.25n, which occurs when the true parameter is p = 0.5. In practice, since p is unknown, the maximum variance is often used for sample size assessments. If a reasonable estimate for p is known the quantity p(1-p) may be used in place of 0.25.

Corso Vittorio Emanuele II) is the only building still extant surely designed by Giovanni Mangone Giovanni Mangone (born towards the end of 15th century, died 25 June 1543) was an Italian artist active almost exclusively in Rome during the Renaissance. Mangone's skills were manifold: he worked as sculptor, architect, stonecutter and building estimator. Moreover, he was a keen antiquarian and among the founders of the Academy dei Virtuosi al Pantheon. As military engineer, he was renowned among his contemporaries.

Due to their sensitivity to outliers, the sample extrema cannot reliably be used as estimators unless data is clean – robust alternatives include the first and last deciles. However, with clean data or in theoretical settings, they can sometimes prove very good estimators, particularly for platykurtic distributions, where for small data sets the mid-range is the most efficient estimator. They are inefficient estimators of location for mesokurtic distributions, such as the normal distribution, and leptokurtic distributions, however.

Base runs (BsR) is a baseball statistic invented by sabermetrician David Smyth to estimate the number of runs a team "should have" scored given their component offensive statistics, as well as the number of runs a hitter or pitcher creates or allows. It measures essentially the same thing as Bill James' runs created, but as sabermetrician Tom M. Tango points out, base runs models the reality of the run-scoring process "significantly better than any other run estimator".

Keith Pollard was born in Kingston upon Hull, East Riding of Yorkshire, England, he has worked as a mechanical estimator, he published his autobiography entitled "Red & White Phoenix - The Adventures Of A Hessle Road Lad" during December 2018, the net proceeds of which go to the Alpha 1-antitrypsin deficiency (A1AD) charity; Alpha-1 UK Support Group, his son Jason had previously died from A1AD, and as of January 2019 he lives in Kingston upon Hull.

He held teaching positions at the University of Minnesota (1959–60), Stanford University (1960–65), Yale University (1965–69), the University of Chicago (1969–74), Northwestern University (1974–82) and the University of Pennsylvania (1982–93). Since 1993 he is part of the faculty of the University of Maryland. A wider known contribution by Nerlove in the field of econometrics is the estimator for the random effects model in panel data analysis, which is implemented in most econometric software packages.

After 1968, Basu began writing polemical essays, which provided paradoxes to frequentist statistics, and which produced great discussion in statistical journals and at statistical meetings. Particularly stimulating papers were Basu's papers on the foundations of survey sampling.Ghosh's editorial notes. There is an extensive literature discussing Basu's problem of estimating the weight of the elephants at a circus with an enormous bull elephant named Jumbo, which Basu used to illustrate his objections to the Horvitz–Thompson estimator and to Fisher's randomisation test.

The MFOE in consisted of five point, 5th order processing of composite real (but altered for declassification) cruise missile data. A window of only 5 data points provided excellent maneuver following; whereas, 5th order processing included fractions of higher order terms to better approximate the complex maneuvering target trajectory. The MFOE overcomes the long-ago rejection of terms higher than 3rd order because, taken at full value (i.e., f_{m}s=1), estimator variances increase exponentially with linear order increases.

In geometry, the Chebyshev center of a bounded set Q having non-empty interior is the center of the minimal-radius ball enclosing the entire set Q, or alternatively (and non-equivalently) the center of largest inscribed ball of Q. In the field of parameter estimation, the Chebyshev center approach tries to find an estimator \hat x for x given the feasibility set Q , such that \hat x minimizes the worst possible estimation error for x (e.g. best worst case).

The Energy Star building energy calculator & targeting tool based on the US IEA and CBECS data from long term US nationwide energy use surveys. This is the estimator that projects use to qualify for a Green Globes rating. It is solid and simple but tells you less about your particular choices – Easy carbon footprint tools, the UK "Footprinter" and "Build Carbon Neutral" These are the simplest of the tools that estimate the total by adding up the easily visible parts.

It is based on two machine learning algorithms: the nearest-neighbor density estimator (NNDE) and the artificial neural network (ANN). NNDE replaces KDE to estimate the updates of bias potential from short biased simulations, while ANN is used to approximate the resulting bias potential. ANN is a memory-efficient representation of high-dimensional functions, where derivatives (biasing forces) are effectively computed with the backpropagation algorithm. An alternative method, exploiting ANN for the adaptive bias potential, uses mean potential forces for the estimation.

The median absolute deviation (also MAD) is the median of the absolute deviation from the median. It is a robust estimator of dispersion. For the example {2, 2, 3, 4, 14}: 3 is the median, so the absolute deviations from the median are {1, 1, 0, 1, 11} (reordered as {0, 1, 1, 1, 11}) with a median of 1, in this case unaffected by the value of the outlier 14, so the median absolute deviation (also called MAD) is 1.

She developed two item response software programs that analyse PISA and TIMSS data; ACER ConQuest (1998) and the R-package TAM (2010). Wu's contributions to the Watterson estimator were uncovered by a team of undergraduate students led by Emilia Huerta-Sánchez (Brown University) and Rori Rohlfs (San Francisco State University). The students searched every issue of Theoretical Population Biology published between 1970 and 1990. She was one of several "acknowledged programmers", all of whom were women, who contributed significantly to highly cited manuscripts.

This implies that the "standard plenoptic camera" may be intended for close range applications as it exhibits increased depth resolution at very close distances that can be metrically predicted based on the camera's parameters.Light field geometry estimator In 2004, a team at Stanford University Computer Graphics Laboratory used a 16-megapixel camera with a 90,000-microlens array (meaning that each microlens covers about 175 pixels, and the final resolution is 90 kilopixels) to demonstrate that pictures can be refocused after they are taken.

The IMM is an estimator which can either be used by MHT or JPDAF. IMM uses two or more Kalman filters which run in parallel, each using a different model for target motion or errors. The IMM forms an optimal weighted sum of the output of all the filters and is able to rapidly adjust to target maneuvers. While MHT or JPDAF handles the association and track maintenance, an IMM helps MHT or JPDAF in obtaining a filtered estimate of the target position.

L-estimators are often statistically resistant, having a high breakdown point. This is defined as the fraction of the measurements which can be arbitrarily changed without causing the resulting estimate to tend to infinity (i.e., to "break down"). The breakdown point of an L-estimator is given by the closest order statistic to the minimum or maximum: for instance, the median has a breakdown point of 50% (the highest possible), and a n% trimmed or Winsorized mean has a breakdown point of n%.

The APES (amplitude and phase estimation) method is also a matched-filter-bank method, which assumes that the phase history data is a sum of 2D sinusoids in noise. APES spectral estimator has 2-step filtering interpretation: # Passing data through a bank of FIR bandpass filters with varying center frequency \omega. # Obtaining the spectrum estimate for \omega \in [0, 2\pi) from the filtered data."Iterative realization of the 2-D Capon method applied in SAR image processing", IET International Radar Conference 2015.

Harold MacDowell is a construction company executive. Born in Muskogee, Oklahoma, MacDowell graduated from high school in Fort Smith, Arkansas, and received his Bachelor's degree in engineering management from Southern Methodist University (SMU) in 1984. He entered the construction industry as an estimator through SMU's School of Engineering Cooperative Education Program and later became a project manager for Wallace Mechanical Corporation. MacDowell is now the CEO of TDIndustries, which was ranked 35 in FORTUNE 's 100 Best Companies to Work For 2008.

A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding of statistical theory and practical knowledge with designing experiments.

The age estimator was developed using 8,000 samples from 82 Illumina DNA methylation array datasets, encompassing 51 healthy tissues and cell types. The major innovation of Horvath's epigenetic clock lies in its wide applicability: the same set of 353 CpGs and the same prediction algorithm is used irrespective of the DNA source within the organism, i.e. it does not require any adjustments or offsets. This property allows one to compare the ages of different areas of the human body using the same aging clock.

Guide to Greece, 4.13.7. The date must have been 724/723 BC if the first year of the first Olympiad was 776/775 BC. Kings Polydorus of the Agiads and Theopompus of the Eurypontids were reigning at that time, roughly in mid-reign. The end of the war must be 379 years from the return of the Heraclids. According to Isaac Newton, also a classical scholar, the nine kings reigned an average of 42 years each, which can be used as an estimator of the dates.

Guide to Greece, 4.13.7. The date must have been 724/723 BC if the first year of the first Olympiad was 776/775 BC. Kings Polydorus of the Agiads and Theopompus of the Eurypontids were reigning at that time, roughly in mid- reign. The end of the war must be 379 years from the return of the Heraclids. According to Isaac Newton, also a classical scholar, the ten kings reigned an average of 38 years each, which can be used as an estimator of the dates.

In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression model. In PCR, instead of regressing the dependent variable on the explanatory variables directly, the principal components of the explanatory variables are used as regressors. One typically uses only a subset of all the principal components for regression, making PCR a kind of regularized procedure and also a type of shrinkage estimator.

The ratio estimator is a statistical parameter and is defined to be the ratio of means of two random variables. Ratio estimates are biased and corrections must be made when they are used in experimental or survey work. The ratio estimates are asymmetrical and symmetrical tests such as the t test should not be used to generate confidence intervals. The bias is of the order O(1/n) (see big O notation) so as the sample size (n) increases, the bias will asymptotically approach 0.

In statistics, consistency of procedures, such as computing confidence intervals or conducting hypothesis tests, is a desired property of their behaviour as the number of items in the data set to which they are applied increases indefinitely. In particular, consistency requires that the outcome of the procedure with unlimited data should identify the underlying truth.Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. (entries for consistency, consistent estimator, consistent test) Use of the term in statistics derives from Sir Ronald Fisher in 1922.

In statistics, the Horvitz–Thompson estimator, named after Daniel G. Horvitz and Donovan J. Thompson,Horvitz, D. G.; Thompson, D. J. (1952) "A generalization of sampling without replacement from a finite universe", Journal of the American Statistical Association, 47, 663–685, . is a method for estimating the totalWilliam G. Cochran (1977), Sampling Techniques, 3rd Edition, Wiley. and mean of a pseudo-population in a stratified sample. Inverse probability weighting is applied to account for different proportions of observations within strata in a target population.

A consulting arm of Beck Technology was formed in 2008 to assist owners, developers, and general contractors with the use of DESTINI Profiler. DESTINI Profiler gives builders the tools to provide real-time cost data and feedback to owners and architects, as well as giving the preconstruction team a major advantage and winning contracts. In 2013, Beck Technology was hired by Sundt Construction to create a new estimating platform to work with DESTINI Profiler data. The result of the project was the first iteration of DESTINI Estimator.

The pseudomedian of a distribution F is defined to be a median of the distribution of (Z_1+Z_2)/2, where Z_1 and Z_2 are independent, each with the same distribution F.Hollander, M. and Wolfe, D. A. (2014). Nonparametric Statistical Methods (3nd Ed.). p58 When F is a symmetric distribution, the pseudomedian coincides with the median, otherwise this is not generally the case. The Hodges–Lehmann statistic, defined as the median of all of the midpoints of pairs of observations, is a consistent estimator of the pseudomedian.

In statistics, the White test is a statistical test that establishes whether the variance of the errors in a regression model is constant: that is for homoskedasticity. This test, and an estimator for heteroscedasticity- consistent standard errors, were proposed by Halbert White in 1980. These methods have become extremely widely used, making this paper one of the most cited articles in economics. In cases where the White test statistic is statistically significant, heteroskedasticity may not necessarily be the cause; instead the problem could be a specification error.

For symmetric distributions, the Hodges–Lehmann statistic has greater efficiency than does the sample median. For the normal distribution, the Hodges-Lehmann statistic is nearly as efficient as the sample mean. For the Cauchy distribution (Student t-distribution with one degree of freedom), the Hodges-Lehmann is infinitely more efficient than the sample mean, which is not a consistent estimator of the median. For non- symmetric populations, the Hodges-Lehmann statistic estimates the population's "pseudo-median", a location parameter that is closely related to the median.

It was used by Peter J. Huber and others working on robust statistics. The L^1-norm was also used in signal processing, for example, in the 1970s, when seismologists constructed images of reflective layers within the earth based on data that did not seem to satisfy the Nyquist–Shannon criterion. It was used in matching pursuit in 1993, the LASSO estimator by Robert Tibshirani in 1996 and basis pursuit in 1998."Atomic decomposition by basis pursuit", by Scott Shaobing Chen, David L. Donoho, Michael, A. Saunders.

The choice of such parametrisation allows good handling of some noise forms and getting comparable measurements; it is essentially the least common denominator with the aid of the bias functions B1 and B2. J. J. Snyder proposed an improved method for frequency or variance estimation, using sample statistics for frequency counters. To get more effective degrees of freedom out of the available dataset, the trick is to use overlapping observation periods. This provides a improvement, and was incorporated in the overlapping Allan variance estimator.

In mathematical statistics, Haar measures are used for prior measures, which are prior probabilities for compact groups of transformations. These prior measures are used to construct admissible procedures, by appeal to the characterization of admissible procedures as Bayesian procedures (or limits of Bayesian procedures) by Wald. For example, a right Haar measure for a family of distributions with a location parameter results in the Pitman estimator, which is best equivariant. When left and right Haar measures differ, the right measure is usually preferred as a prior distribution.

The best example of the plug- in principle, the bootstrapping method. Bootstrapping is a statistical method for estimating the sampling distribution of an estimator by sampling with replacement from the original sample, most often with the purpose of deriving robust estimates of standard errors and confidence intervals of a population parameter like a mean, median, proportion, odds ratio, correlation coefficient or regression coefficient. It has been called the plug-in principle,Logan, J. David and Wolesensky, Willian R. Mathematical methods in biology. Pure and Applied Mathematics: a Wiley-interscience Series of Texts, Monographs, and Tracts.

While subsampling was originally proposed for the case of independent and identically distributed (iid) data only, the methodology has been extended to cover time series data as well; in this case, one resamples blocks of subsequent data rather than individual data points. There are many cases of applied interest where subsampling leads to valid inference whereas bootstrapping does not; for example, such cases include examples where the rate of convergence of the estimator is not the square root of the sample size or when the limiting distribution is non-normal.

DeMatteis graduated from Ashland College in 1989, majoring in mathematics and economics; she credits Ashland mathematics professor Alan G. Poorman with her decision to study mathematics there. After earning a master's degree in statistics from Miami University in Ohio, she became a Bureau of Labor Statistics researcher from 1991 to 1995. She moved to Westat in 1995 and returned to graduate study, completing her Ph.D. at American University in 1998. Her dissertation, All- Cases Imputation Variance Estimator: A New Approach to Variance Estimation for Imputed Data, was supervised by Robert Jernigan.

Analysing Early Observations, IMSS Florence But perhaps, as it often happens in Science, it was the availability or the insight of a good theory to allow Huygens a better representation of the whole Saturn's system. Unfortunately Huygens's attitude offended Divini and provoked a series of attacks and retorts that led to mutual insults. As Divini was unable to write in Latin, he asked Honoré Fabri (a powerful French Jesuit anti-Copernican who lived in Rome and was user-estimator of Divini's telescopes) to translate his defense of the effectiveness of his own telescopes.

The coefficients change each season based upon how often each event occurs. Because the coefficients are derived from expected run value, we can use wOBA to estimate a few more things about a player's production and baseball as a whole. When using the formula (shown below), the numerator side on its own will give us an estimate of how many runs a player is worth to his team. Similarly, a team's wOBA is a good estimator of team runs scored, and deviations from predicted runs scored indicate a combination of situational hitting and base running.

This form of the formula is limited to between-subjects analysis with equal sample sizes in all cells. Since it is less biased (although not unbiased), ω2 is preferable to η2; however, it can be more inconvenient to calculate for complex analyses. A generalized form of the estimator has been published for between-subjects and within-subjects analysis, repeated measure, mixed design, and randomized block design experiments. In addition, methods to calculate partial ω2 for individual factors and combined factors in designs with up to three independent variables have been published.

Modern statistical meta- analysis does more than just combine the effect sizes of a set of studies using a weighted average. It can test if the outcomes of studies show more variation than the variation that is expected because of the sampling of different numbers of research participants. Additionally, study characteristics such as measurement instrument used, population sampled, or aspects of the studies' design can be coded and used to reduce variance of the estimator (see statistical models above). Thus some methodological weaknesses in studies can be corrected statistically.

The papers establishing the mathematical foundations of Kalman type filters were published between 1959 and 1961. The Kalman filter is the optimal linear estimator for linear system models with additive independent white noise in both the transition and the measurement systems. Unfortunately, in engineering, most systems are nonlinear, so attempts were made to apply this filtering method to nonlinear systems; Most of this work was done at NASA Ames. The EKF adapted techniques from calculus, namely multivariate Taylor series expansions, to linearize a model about a working point.

When the observations come from an exponential family and mild conditions are satisfied, least-squares estimates and maximum-likelihood estimates are identical. The method of least squares can also be derived as a method of moments estimator. The following discussion is mostly presented in terms of linear functions but the use of least squares is valid and practical for more general families of functions. Also, by iteratively applying local quadratic approximation to the likelihood (through the Fisher information), the least- squares method may be used to fit a generalized linear model.

The data are also subject to errors, and the errors in b are also assumed to be independent with zero mean and standard deviation \sigma _b. Under these assumptions the Tikhonov-regularized solution is the most probable solution given the data and the a priori distribution of x, according to Bayes' theorem. If the assumption of normality is replaced by assumptions of homoscedasticity and uncorrelatedness of errors, and if one still assumes zero mean, then the Gauss–Markov theorem entails that the solution is the minimal unbiased linear estimator.

That is, the method derandomizes the proof. The basic idea is to replace each random choice in a random experiment by a deterministic choice, so as to keep the conditional probability of failure, given the choices so far, below 1. The method is particularly relevant in the context of randomized rounding (which uses the probabilistic method to design approximation algorithms). When applying the method of conditional probabilities, the technical term pessimistic estimator refers to a quantity used in place of the true conditional probability (or conditional expectation) underlying the proof.

This explains why the normal distribution can be used successfully for certain data sets of ratios. Another related distribution is the log-harmonic law, which is the probability distribution of a random variable whose logarithm follows an harmonic law. This family has an interesting property, the Pitman estimator of the location parameter does not depend on the choice of the loss function. Only two statistical models satisfy this property: One is the normal family of distributions and the other one is a three-parameter statistical model which contains the log-harmonic law.

Robust optimization is an approach to solve optimization problems under uncertainty in the knowledge of underlying parameters,. For instance, the MMSE Bayesian estimation of a parameter requires the knowledge of parameter correlation function. If the knowledge of this correlation function is not perfectly available, a popular minimax robust optimization approach is to define a set characterizing the uncertainty about the correlation function, and then pursuing a minimax optimization over the uncertainty set and the estimator respectively. Similar minimax optimizations can be pursued to make estimators robust to certain imprecisely known parameters.

Like all estimators based on moments of the Jeans equations, the Leonard–Merritt estimator requires an assumption about the relative distribution of mass and light. As a result, it is most useful when applied to stellar systems that have one of two properties: # All or almost all of the mass resides in a central object, or, # the mass is distributed in the same way as the observed stars. Case (1) applies to the nucleus of a galaxy containing a supermassive black hole. Case (2) applies to a stellar system composed entirely of luminous stars (i.e.

An alternative method of reducing or eliminating the bias in the ratio estimator is to alter the method of sampling. The variance of the ratio using these methods differs from the estimates given previously. Note that while many applications such as those discussion in Lohr are intended to be restricted to positive integers only, such as sizes of sample groups, the Midzuno-Sen method works for any sequence of positive numbers, integral or not. It's not clear what it means that Lahiri's method works since it returns a biased result.

Recently, algorithms based on sequential Monte Carlo methods have been used to approximate the conditional mean of the outputs or, in conjunction with the Expectation-Maximization algorithm, to approximate the maximum likelihood estimator. These methods, albeit asymptotically optimal, are computationally demanding and their use is limited to specific cases where the fundamental limitations of the employed particle filters can be avoided. An alternative solution is to apply the prediction error method using a sub-optimal predictor.M. Abdalmoaty, ‘Learning Stochastic Nonlinear Dynamical Systems Using Non-stationary Linear Predictors’, Licentiate dissertation, Stockholm, Sweden, 2017.

H. P. Young, "Group choice and individual judgements", Chapter 9 of Perspectives on public choice: a handbook, edited by Dennis Mueller (1997) Cambridge UP., pp.181 -200. Young adopted an epistemic approach to preference-aggregation: he supposed that there was an objectively 'correct', but unknown preference order over the alternatives, and voters receive noisy signals of this true preference order (cf. Condorcet's jury theorem.) Using a simple probabilistic model for these noisy signals, Young showed that the Kemeny–Young method was the maximum likelihood estimator of the true preference order.

A. Touloumis (2015) "Nonparametric Stein-type shrinkage covariance matrix estimators in high-dimensional settings" Computational Statistics & Data Analysis 83: 251—261.O. Ledoit and M. Wolf (2003) "Improved estimation of the covariance matrix of stock returns with an application to portofolio selection " Journal of Empirical Finance 10 (5): 603—621.O. Ledoit and M. Wolf (2004b) "Honey, I shrunk the sample covariance matrix " The Journal of Portfolio Management 30 (4): 110—119.. One considers a convex combination of the empirical estimator (A) with some suitable chosen target (B), e.g.

In 1866, Deen Dayal entered government service as head estimator and draughtsman in the Department of Works Secretariat Office in Indore. Meanwhile, he took up photography. His first patron in Indore was Maharaja Tukoji Rao II of Indore state, who in turn introduced him to Sir Henry Daly, agent to the Governor General for Central India (1871–1881) and the founder of Daly College, who encouraged his work, along with the Maharaja himself who encouraged him to set up his studio in Indore. Soon he was getting commissions from Maharajas and the British Raj.

One is to use a pseudo inverse instead of the usual matrix inverse in the above formulae. However, better numeric stability may be achieved by first projecting the problem onto the subspace spanned by \Sigma_b . Another strategy to deal with small sample size is to use a shrinkage estimator of the covariance matrix, which can be expressed mathematically as : \Sigma = (1-\lambda) \Sigma+\lambda I\, where I is the identity matrix, and \lambda is the shrinkage intensity or regularisation parameter. This leads to the framework of regularized discriminant analysis or shrinkage discriminant analysis.

Many different derivations of the above formula for p_r have been given. One of the simplest ways to motivate the formula is by assuming the next item will behave similarly to the previous item. The overall idea of the estimator is that currently we are seeing never-seen items at a certain frequency, seen-once items at a certain frequency, seen-twice items at a certain frequency, and so on. Our goal is to estimate just how likely each of these categories is, for the next item we will see.

SCoPE/Slick Cosmological Parameter Estimator is a newly developed cosmological MCMC package written by Santanu Das in C language. Apart from standard global metropolis algorithm the code uses three unique technique named as 'delayed rejection' that increases the acceptance rate of a chain, 'pre-fetching' that helps an individual chain to run on parallel CPUs and 'inter-chain covariance update' that prevents clustering of the chains allowing faster and better mixing of the chains. The code is capable of faster computation of cosmological parameters from WMAP and Planck data.

In 2002, scarlet fever was reported to be in Korean children in the Jeju Province. Scientists have been doing research on the matter by creating an age-period-cohort (APC) analysis to back up their relevant hypotheses regarding this emerging outbreak. The Korean National Health Insurance Service analyzed this data from the nationwide insurance claims. Their calculations of the crude incidence rate (CIR) and applying the intrinsic estimator (IE) for age and calendar groups revealed that a total of 2,345 cases of children had the fever that was one of the top illnesses.

In the Bayesian approach, such prior information is captured by the prior probability density function of the parameters; and based directly on Bayes theorem, it allows us to make better posterior estimates as more observations become available. Thus unlike non-Bayesian approach where parameters of interest are assumed to be deterministic, but unknown constants, the Bayesian estimator seeks to estimate a parameter that is itself a random variable. Furthermore, Bayesian estimation can also deal with situations where the sequence of observations are not necessarily independent. Thus Bayesian estimation provides yet another alternative to the MVUE.

Maximum likelihood estimators (MLE) are thus a special case of M-estimators. With suitable rescaling, M-estimators are special cases of extremum estimators (in which more general functions of the observations can be used). The function ρ, or its derivative, ψ, can be chosen in such a way to provide the estimator desirable properties (in terms of bias and efficiency) when the data are truly from the assumed distribution, and 'not bad' behaviour when the data are generated from a model that is, in some sense, close to the assumed distribution.

Hansen is known for his research on volatility, forecasting and cointegration, including the "test for superior predictive ability", which can be used to test whether a benchmark forecast is significantly outperformed by competing forecasts, the Model Confidence Set. He has, in collaboration with Ole E. Barndorff-Nielsen, Asger Lunde, and Neil Shephard, developed the realized kernel estimator that can estimate the quadratic variation in an environment with noisy high-frequency data, such as financial tick-by-tick data. He co-authored the book "Workbook on Cointegration" with Søren Johansen.

Often, if just a little bias is permitted, then an estimator can be found with lower MSE and/or fewer outlier sample estimates. An alternative to the version of "unbiased" above, is "median-unbiased", where the median of the distribution of estimates agrees with the true value; thus, in the long run half the estimates will be too low and half too high. While this applies immediately only to scalar-valued estimators, it can be extended to any measure of central tendency of a distribution: see median-unbiased estimators.

These robust estimators typically have inferior statistical efficiency compared to conventional estimators for data drawn from a distribution without outliers (such as a normal distribution), but have superior efficiency for data drawn from a mixture distribution or from a heavy-tailed distribution, for which non-robust measures such as the standard deviation should not be used. For example, for data drawn from the normal distribution, the MAD is 37% as efficient as the sample standard deviation, while the Rousseeuw–Croux estimator Qn is 88% as efficient as the sample standard deviation.

A mixture of two unimodal distributions with differing means is not necessarily bimodal. The combined distribution of heights of men and women is sometimes used as an example of a bimodal distribution, but in fact the difference in mean heights of men and women is too small relative to their standard deviations to produce bimodality. Bimodal distributions have the peculiar property that – unlike the unimodal distributions – the mean may be a more robust sample estimator than the median. This is clearly the case when the distribution is U shaped like the arcsine distribution.

For each such subset, the mean is computed; finally, the median of these n(n + 1)/2 averages is defined to be the Hodges–Lehmann estimator of location. The Hodges–Lehmann statistic also estimates the difference between two populations. For two sets of data with m and n observations, the set of two-element sets made of them is their Cartesian product, which contains m × n pairs of points (one from each set); each such pair defines one difference of values. The Hodges–Lehmann statistic is the median of the m × n differences.

Lombriser's research is in Theoretical Cosmology, Dark Energy, and Alternative Theories of Gravity. In 2010 he was part of a research group that succeeded to conduct the first measurement of the E_G quantity, a model- independent estimator for gravitational interactions on cosmological distances. In 2015 and 2016, Lombriser predicted the measurement of the gravitational wave speed with a neutron star merger and that this would rule out alternative theories of gravity as the cause of the late-time accelerated expansion of our Universe. This prediction and its implications became reality with GW170817.

A real estate appraisal is like any other statistical sampling process. The comparables are the samples drawn and measured, and the outcome is an estimate of value—called an "opinion of value" in the terminology of real estate appraisal. In most statistical sampling processes, a single best estimator is sought. However, since real estate markets are known to be highly inefficient, and market transaction data is subject to significant error, the appraisal process generally relies on multiple simultaneous approaches to value, with a judgmental reconciliation as the final step to arrive at the appraiser's opinion.

In 2011, Apax Partners purchased both Activant and Epicor and merged the organizations together. Pervez Qureshi, prior CEO of Activant, became CEO of the new Epicor in May, 2011. In April 2012, Epicor partnered with ASA Automotive Systems Inc. to help ASA dealers increase vehicle parts and service revenue with Epicor Integrated Service Estimator. In October 2012, Epicor acquired Solarsoft Business Systems, established in 2007 from the merger of CMS Software Inc. of Toronto and XKO Software Ltd from the UK. Before the acquisition, Solarsoft acquired Progressive Solutions in June 2012.

Before moving to New York, Ralescu was an assistant professor in the Division of Applied Mathematics at Brown University (1981–1984). His research themes are varied, with noteworthy contributions in the fields of asymptotic theory of perturbed empirical and quantile processes, nonparametric density estimation and Stein estimation (see James–Stein estimator). Other applied work that received praise was written up in collaboration with Dr. A. Cassvan in connection to techniques using brain auditory evoked potentials (BAEP). The paper "Brainstem auditory evoked potential studies in patients with tinnitus and/or vertigo" is a standard reference.

The alternative estimators have been characterized into two general type: (1) robust and (2) limited information estimator. When ML is implemented with data that deviates away from the assumptions of normal theory, CFA models may produce biased parameter estimates and misleading conclusions. Robust estimation typically attempts to correct the problem by adjusting the normal theory model χ2 and standard errors. For example, Satorra and Bentler (1994) recommended using ML estimation in the usual way and subsequently dividing the model χ2 by a measure of the degree of multivariate kurtosis.

When performing a statistical test such as Tajima's D, the critical question is whether the value calculated for the statistic is unexpected under a null process. For Tajima's D, the magnitude of the statistic is expected to increase the more the data deviates from a pattern expected under a population evolving according to the standard coalescent model. Tajima (1989) found an empirical similarity between the distribution of the test statistic and a beta distribution with mean zero and variance one. He estimated theta by taking Watterson's estimator and dividing it by the number of samples.

Hii's professional theatre debut was with the Queensland Theatre Company's production of The Estimator in 2007, after he was noticed by its playwright David Brown performing in a play reading with The Emerge Project. He was later cast in guest roles in the television series East of Everything and H2O: Just Add Water. In 2011, Hii appeared as Tom in the short film Kiss. Hii appeared in the lead role of Van Tuong Nguyen in SBS's four-part miniseries Better Man, which began airing from 25 July 2013.

There are cases when a sample is taken without knowing, in advance, how many observations will be acceptable according to some criterion. In such cases, the sample size N is a random variable whose variation adds to the variation of X, such that, :Var(∑X) = E(N)Var(X) + Var(N)E2(X).Cornell, J R, and Benjamin, C A, Probability, Statistics, and Decisions for Civil Engineers, McGraw-Hill, NY, 1970, pp.178-9. If N has a Poisson distribution, then E(N) = Var(N) with estimator N = n.

This estimator can be interpreted as a weighted average between the noisy measurements y and the prior expected value m. If the noise variance \sigma_w^2 is low compared with the variance of the prior \sigma_x^2 (corresponding to a high SNR), then most of the weight is given to the measurements y, which are deemed more reliable than the prior information. Conversely, if the noise variance is relatively higher, then the estimate will be close to m, as the measurements are not reliable enough to outweigh the prior information.

In a data-aided approach, the channel estimation is based on some known data, which is known both at the transmitter and at the receiver, such as training sequences or pilot data. In a blind approach, the estimation is based only on the received data, without any known transmitted sequence. The tradeoff is the accuracy versus the overhead. A data-aided approach requires more bandwidth or it has a higher overhead than a blind approach, but it can achieve a better channel estimation accuracy than a blind estimator.

James Barnes significantly extended the work on bias functions, introducing the modern B1 and B2 bias functions. Curiously enough, it refers to the M-sample variance as "Allan variance", while referring to Allan's article "Statistics of Atomic Frequency Standards". With these modern bias functions, full conversion among M-sample variance measures of various M, T and τ values could be performed, by conversion through the 2-sample variance. James Barnes and David Allan further extended the bias functions with the B3 function to handle the concatenated samples estimator bias.

Note that winsorizing is not equivalent to simply excluding data, which is a simpler procedure, called trimming or truncation, but is a method of censoring data. In a trimmed estimator, the extreme values are discarded; in a winsorized estimator, the extreme values are instead replaced by certain percentiles (the trimmed minimum and maximum). Thus a winsorized mean is not the same as a truncated mean. For instance, the 10% trimmed mean is the average of the 5th to 95th percentile of the data, while the 90% winsorized mean sets the bottom 5% to the 5th percentile, the top 5% to the 95th percentile, and then averages the data. In the previous example the trimmed mean would be obtained from the smaller set: :{92, 19, 101, 58, 91, 26, 78, 10, 13, 101, 86, 85, 15, 89, 89, 28, −5, 41} (N = 18, mean = 56.5) In this case, the winsorized mean can equivalently be expressed as a weighted average of the truncated mean and the 5th and 95th percentiles (for the 10% winsorized mean, 0.05 times the 5th percentile, 0.9 times the 10% trimmed mean, and 0.05 times the 95th percentile) though in general winsorized statistics need not be expressible in terms of the corresponding trimmed statistic.

When estimating the cost for a project, product or other item or investment, there is always uncertainty as to the precise content of all items in the estimate, how work will be performed, what work conditions will be like when the project is executed and so on. These uncertainties are risks to the project. Some refer to these risks as "known-unknowns" because the estimator is aware of them, and based on past experience, can even estimate their probable costs. The estimated costs of the known-unknowns is referred to by cost estimators as cost contingency.

Kernel regression also was introduced in partially linear model. The local constant method, which is developed by Speckman, and local linear techniques, which was found by Hamilton and Truong in 1997 and was revised by Opsomer and Ruppert in 1997, are all included in kernel regression. Green et al, Opsomer and Ruppert found that one of the significant characteristic of kernel-based methods is that under-smoothing has been taken in order to find root-n estimator of beta. However, Speckman’s research in 1988 and Severini’s and Staniswalis’s research in 1994 proved that those restriction might be canceled.

Eta-squared describes the ratio of variance explained in the dependent variable by a predictor while controlling for other predictors, making it analogous to the r2. Eta-squared is a biased estimator of the variance explained by the model in the population (it estimates only the effect size in the sample). This estimate shares the weakness with r2 that each additional variable will automatically increase the value of η2. In addition, it measures the variance explained of the sample, not the population, meaning that it will always overestimate the effect size, although the bias grows smaller as the sample grows larger.

The most widely used method to estimate between studies variance (REVC) is the DerSimonian-Laird (DL) approach. Several advanced iterative (and computationally expensive) techniques for computing the between studies variance exist (such as maximum likelihood, profile likelihood and restricted maximum likelihood methods) and random effects models using these methods can be run in Stata with the metaan command. The metaan command must be distinguished from the classic metan (single "a") command in Stata that uses the DL estimator. These advanced methods have also been implemented in a free and easy to use Microsoft Excel add-on, MetaEasy.

The estimator can be computed in time from the two signatures of the given sets, in either variant of the scheme. Therefore, when and are constants, the time to compute the estimated similarity from the signatures is also constant. The signature of each set can be computed in linear time on the size of the set, so when many pairwise similarities need to be estimated this method can lead to a substantial savings in running time compared to doing a full comparison of the members of each set. Specifically, for set size the many hash variant takes time.

Zippin’s doctoral thesis became the basis for the Zippin Estimator, a mathematical procedure for estimating wildlife population size based on capture and removal of sequentially trapped animal samples. The method was explored by P. A. P. Moran (1951) and its properties elaborated by Zippin in 1956 and 1958. Zippin has done extensive research on cancer staging, particularly cancer of the breastand colon-rectum with the American Joint Committee on Cancer and the International Union Against Cancer. He has published on the epidemiology of breast, uterine, and nasopharyngeal cancer, late effects of radiation, and survival patterns in acute lymphocytic and chronic lymphocytic leukemia.

Cost of War are real-time cost-estimation exhibits, each featuring a counter/estimator for the Iraq War and the Afghanistan War. These exhibits are maintained by the National Priorities Project.Official Site; National Priorities Project As of June 1, 2010 both wars had a combined estimated cost of over 1 trillion dollars, separately the Iraq War had an estimated cost of 725 billion dollars and the Afghanistan War had an estimated cost of 276 billion dollars. The numbers are based on US Congress appropriation reports and do not include "future medical care for soldiers and veterans wounded in the war".

John Philip Rust (born May 23, 1955) is an American economist and econometrician. John Rust received his PhD from MIT in 1983 and taught at the University of Wisconsin, Yale University and University of Maryland before joining Georgetown University in 2012. John Rust was awarded Frisch Medal in 1992 and became the fellow of Econometric Society in 1993. John Rust is best known as one of the founding fathers of the structural estimation of dynamic discrete choice models and the developer of the nested fixed point (NFXP) maximum likelihood estimator which is widely used in structural econometrics.

Institutions such as the International Energy Agency (IEA), the U.S. Energy Information Administration (EIA), and the European Environment Agency (EEA) record and publish energy data periodically. Improved data and understanding of world energy consumption may reveal systemic trends and patterns, which could help frame current energy issues and encourage movement towards collectively useful solutions. Closely related to energy consumption is the concept of total primary energy supply (TPES), which – on a global level – is the sum of energy production minus storage changes. Since changes of energy storage over the year are minor, TPES values can be used as an estimator for energy consumption.

Although new approaches have since been found, McDermott turned to other areas of AI, such as vision and robotics, and began working on automated planning again. His work on planning focused on the "classical" case rather than on hierarchical task network planning. In 1990 he was named a Fellow of the Association for the Advancement of Artificial Intelligence, one of the first group of Fellows. In 1996 he (and Hector Geffner and Blai Bonet independently) discovered "estimated-regression planning", based on the idea of heuristic search with an estimator derived from a simplified domain model by reasoning backward ("regression") from the goal.

He knew that there were around 13,000 funerals per year in London and that three people died per eleven families per year. He estimated from the parish records that the average family size was 8 and calculated that the population of London was about 384,000; this is the first known use of a ratio estimator. Laplace in 1802 estimated the population of France with a similar method; see for details. Although the original scope of statistics was limited to data useful for governance, the approach was extended to many fields of a scientific or commercial nature during the 19th century.

The trimmed mean is a simple robust estimator of location that deletes a certain percentage of observations (10% here) from each end of the data, then computes the mean in the usual way. The analysis was performed in R and 10,000 bootstrap samples were used for each of the raw and trimmed means. The distribution of the mean is clearly much wider than that of the 10% trimmed mean (the plots are on the same scale). Also whereas the distribution of the trimmed mean appears to be close to normal, the distribution of the raw mean is quite skewed to the left.

Each symbol is modulated by gradually changing the phase of the carrier from the starting value to the final value, over the symbol duration. The modulation and demodulation of CPM is complicated by the fact that the initial phase of each symbol is determined by the cumulative total phase of all previous transmitted symbols, which is known as the phase memory. Therefore, the optimal receiver cannot make decisions on any isolated symbol without taking the entire sequence of transmitted symbols into account. This requires a maximum- likelihood sequence estimator (MLSE), which is efficiently implemented using the Viterbi algorithm.

On July 22, 2008, the Social Security Administration introduced a new online benefits estimator. A worker who has enough Social Security credits to qualify for benefits, but who is not currently receiving benefits on his or her own Social Security record and who is not a Medicare beneficiary, can obtain an estimate of the retirement benefit that will be provided, for different assumptions about age at retirement. This process is done by opening a secure online account called my Social Security. For retirees who have non FICA or SECA taxed wages the rules get complicated and probably require additional help.

In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population mean). More formally, it is the application of a point estimator to the data to obtain a point estimate. Point estimation can be contrasted with interval estimation: such interval estimates are typically either confidence intervals, in the case of frequentist inference, or credible intervals, in the case of Bayesian inference.

In statistics, the Hájek–Le Cam convolution theorem states that any regular estimator in a parametric model is asymptotically equivalent to a sum of two independent random variables, one of which is normal with asymptotic variance equal to the inverse of Fisher information, and the other having arbitrary distribution. The obvious corollary from this theorem is that the “best” among regular estimators are those with the second component identically equal to zero. Such estimators are called efficient and are known to always exist for regular parametric models. The theorem is named after Jaroslav Hájek and Lucien Le Cam.

Theil is most famous for his invention of the widely used two-stage least squares (2SLS) method in 1953. This estimation technique greatly simplified estimation of simultaneous equation models of the economy and came into widespread use for this purpose. He is also famous for the Theil index, a measure of entropy, which belongs to the class of Kolm-Indices and is used as an inequity indicator in econometrics.Cowell, Frank A. (2002, 2003): Theil, Inequality and the Structure of Income Distribution, London School of Economics and Political Sciences He is also responsible for the Theil–Sen estimator for robust regression.

In ecology, plot sampling is a method of abundance estimation in which plots are selected from within a survey region and sampled; population estimates can then be made using the Horvitz–Thompson estimator. Generally plot sampling is a useful method if it can be assumed that each survey will identify all of the animals in the sampled area, and that the animals will be distributed uniformly and independently. If the entire survey region is covered in this manner, rather than a subset of plots that are then used for extrapolation, this is considered a census rather than a plot sampling approach.

Statistical estimators will calculate an estimated value on the sample series used. The estimates may deviate from the true value and the range of values which for some probability will contain the true value is referred to as the confidence interval. The confidence interval depends on the number of observations in the sample series, the dominant noise type, and the estimator being used. The width is also dependent on the statistical certainty for which the confidence interval values forms a bounded range, thus the statistical certainty that the true value is within that range of values.

Critical for the solution of certain differential equations, these functions are used throughout both classical and quantum physics. Bessel is responsible for the correction to the formula for the sample variance estimator named in his honour. This is the use of the factor n − 1 in the denominator of the formula, rather than just n. This occurs when the sample mean rather than the population mean is used to centre the data and since the sample mean is a linear combination of the data the residual to the sample mean overcounts the number of degrees of freedom by the number of constraint equations — in this case one.

As a quantitative measure, the "forecast bias" can be specified as a probabilistic or statistical property of the forecast error. A typical measure of bias of forecasting procedure is the arithmetic mean or expected value of the forecast errors, but other measures of bias are possible. For example, a median- unbiased forecast would be one where half of the forecasts are too low and half too high: see Bias of an estimator. In contexts where forecasts are being produced on a repetitive basis, the performance of the forecasting system may be monitored using a tracking signal, which provides an automatically maintained summary of the forecasts produced up to any given time.

A simple, very important example of a generalized linear model (also an example of a general linear model) is linear regression. In linear regression, the use of the least-squares estimator is justified by the Gauss–Markov theorem, which does not assume that the distribution is normal. From the perspective of generalized linear models, however, it is useful to suppose that the distribution function is the normal distribution with constant variance and the link function is the identity, which is the canonical link if the variance is known. For the normal distribution, the generalized linear model has a closed form expression for the maximum-likelihood estimates, which is convenient.

Calvin Zippin (born July 17, 1926) is a cancer epidemiologist and biostatistician, and Professor Emeritus in the Department of Epidemiology and Biostatistics at the University of California School of Medicine in San Francisco (UCSF). He is a Fellow of the American Statistical Association, the American College of Epidemiologyand the Royal Statistical Society of Great Britain. His doctoral thesis was the basis for the Zippin Estimator, a procedure for estimating wildlife populations using data from trapping experiments. He was a principal investigator in the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute (NCI) which assesses the magnitude and nature of the cancer problem in the United States.

The goal of the Wiener filter is to compute a statistical estimate of an unknown signal using a related signal as an input and filtering that known signal to produce the estimate as an output. For example, the known signal might consist of an unknown signal of interest that has been corrupted by additive noise. The Wiener filter can be used to filter out the noise from the corrupted signal to provide an estimate of the underlying signal of interest. The Wiener filter is based on a statistical approach, and a more statistical account of the theory is given in the minimum mean square error (MMSE) estimator article.

A statistically significant correlation between penis size and the size of other body parts has not been found in research. One study, Siminoski and Bain (1988), found a weak correlation between the size of the stretched penis and foot size and height; however, it was too weak to be used as a practical estimator. Another investigation, Shah and Christopher (2002), which cited Siminoski and Bain (1988), failed to find any evidence for a link between shoe size and stretched penis size, stating "the supposed association of penile length and shoe size has no scientific basis". There may be a link between the malformation of the genitalia and the human limbs.

The first known use of the ratio estimator was by John Graunt in England who in 1662 was the first to estimate the ratio y/x where y represented the total population and x the known total number of registered births in the same areas during the preceding year. Later Messance (~1765) and Moheau (1778) published very carefully prepared estimates for France based on enumeration of population in certain districts and on the count of births, deaths and marriages as reported for the whole country. The districts from which the ratio of inhabitants to birth was determined only constituted a sample. In 1802, Laplace wished to estimate the population of France.

The empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment. In a more general sense, empirical probability estimates probabilities from experience and observation. Given an event A in a sample space, the relative frequency of A is the ratio m/n, m being the number of outcomes in which the event A occurs, and n being the total number of outcomes of the experiment. In statistical terms, the empirical probability is an estimate or estimator of a probability.

Over time, moving targets will impose a changing Doppler shift and direction of arrival on the CW tone that is characteristic of the location, speed and heading of the target. It is therefore possible to use a non-linear estimator to estimate the state of the target from the time history of the Doppler and bearing measurements. Work has been published that has demonstrated the feasibility of this approach for tracking aircraft using the vision carrier of analogue television signals. However, track initiation is slow and difficult, and so the use of narrow band signals is probably best considered as an adjunct to the use of illuminators with better ambiguity surfaces.

Delaunay triangulations can be used to determine the density or intensity of points samplings by means of the Delaunay tessellation field estimator (DTFE). A Delaunay triangulation of a random set of 100 points in a plane. Delaunay triangulations are often used to generate meshes for space-discretised solvers such as the finite element method and the finite volume method of physics simulation, because of the angle guarantee and because fast triangulation algorithms have been developed. Typically, the domain to be meshed is specified as a coarse simplicial complex; for the mesh to be numerically stable, it must be refined, for instance by using Ruppert's algorithm.

Steel, R.G.D, and Torrie, J. H., Principles and Procedures of Statistics with Special Reference to the Biological Sciences., McGraw Hill, 1960, page 288. Although the MSE (as defined in this article) is not an unbiased estimator of the error variance, it is consistent, given the consistency of the predictor. In regression analysis, "mean squared error", often referred to as mean squared prediction error or "out-of-sample mean squared error", can also refer to the mean value of the squared deviations of the predictions from the true values, over an out-of-sample test space, generated by a model estimated over a particular sample space.

He subsequently took a job as a drafter with the Chicago and North Western Transportation Company (C&NWRR;) from 1900 to 1903, then worked with architect George Fuller on a C&NWRR; office building for two years. He returned to school and earned an architectural degree at MIT in 1907. After a brief stint in Chicago, Naramore moved to Portland, Oregon, where he worked for Northwest Bridgeworks from 1909 to 1912 as a cost estimator. Naramore's involvement with schools began thereafter and lasted until the 1930s. He was appointed Architect and Superintendent of properties for the Portland School District, a job he held from 1912 to 1919.

Cost overruns with government projects have occurred when the contractor identified change orders or project changes that increased costs, which are not subject to competition from other firms as they have already been eliminated from consideration after the initial bid. Fraud is also an occasional construction issue. Large projects can involve highly complex financial plans and often start with a conceptual estimate performed by a building estimator. As portions of a project are completed, they may be sold, supplanting one lender or owner for another, while the logistical requirements of having the right trades and materials available for each stage of the building construction project carries forward.

One of the most popular applications of wavelet transform is image compression. The advantage of using wavelet-based coding in image compression is that it provides significant improvements in picture quality at higher compression ratios over conventional techniques. Since wavelet transform has the ability to decompose complex information and patterns into elementary forms, it is commonly used in acoustics processing and pattern recognition, but it has been also proposed as an instantaneous frequency estimator. Moreover, wavelet transforms can be applied to the following scientific research areas: edge and corner detection, partial differential equation solving, transient detection, filter design, electrocardiogram (ECG) analysis, texture analysis, business information analysis and gait analysis.

A plot of the Kaplan–Meier estimator is a series of declining horizontal steps which, with a large enough sample size, approaches the true survival function for that population. The value of the survival function between successive distinct sampled observations ("clicks") is assumed to be constant. An important advantage of the Kaplan–Meier curve is that the method can take into account some types of censored data, particularly right-censoring, which occurs if a patient withdraws from a study, is lost to follow-up, or is alive without event occurrence at last follow-up. On the plot, small vertical tick-marks state individual patients whose survival times have been right-censored.

Research has shown that Bayesian methods that involve a Poisson likelihood function and an appropriate prior probability (e.g., a smoothing prior leading to total variation regularization or a Laplacian distribution leading to \ell_1-based regularization in a wavelet or other domain), such as via Ulf Grenander's Sieve estimator or via Bayes penalty methods or via I.J. Good's roughness method may yield superior performance to expectation-maximization- based methods which involve a Poisson likelihood function but do not involve such a prior. Attenuation correction: Quantitative PET Imaging requires attenuation correction. In these systems attenuation correction is based on a transmission scan using 68Ge rotating rod source.

SGLD can be applied to the optimization of non-convex objective functions, shown here to be a sum of Gaussians. Stochastic gradient Langevin dynamics (SGLD), is an optimization technique composed of characteristics from Stochastic gradient descent, a Robbins–Monro optimization algorithm, and Langevin dynamics, a mathematical extension of molecular dynamics models. Like stochastic gradient descent, SGLD is an iterative optimization algorithm which introduces additional noise to the stochastic gradient estimator used in SGD to optimize a differentiable objective function. Unlike traditional SGD, SGLD can be used for Bayesian learning, since the method produces samples from a posterior distribution of parameters based on available data.

The inputs to the algorithm are two waveforms represented by two data vectors containing 16 bit PCM samples. The first vector contains the samples of the (undistorted) reference signal, whereas the second vector contains the samples of the degraded signal. The POLQA algorithm consists of a temporal alignment block, a sample rate estimator of a sample rate converter, which is used to compensate for differences in the sample rate of the input signals, and the actual core model, which performs the MOS calculation. In a first step, the delay between the two input signals is determined and the sample rate of the two signals relative to each other is estimated.

For indoor environments such as offices or gyms where the principal source of CO2 is human respiration, rescaling some easier-to-measure quantities such as volatile organic compound (VOC) and hydrogen gas (H2) concentrations provides a good-enough estimator of the current CO2 concentration for ventilation and occupancy purposes. Sensors for these substances can be made using cheap (~$20) MEMS metal oxide semiconductor (MOS) technology. The reading they generate is called estimated CO2 (eCO2) or CO2 equivalent (CO2eq). Although the readings tend to be good enough in the long run, introducing non-respiration sources of VOC or CO2, such as peeling fruits or using perfume, will undermine their reliability.

He worked at a curtain factory before landing a job as an estimator for a general contractor. Noticing that most contractors turned down work on the New York waterfront because it was difficult and dirty work, he started his own firm and was able to underbid the few competitors he had. After winning and successfully completing many jobs, his reputation allowed him to win larger projects around the city and then nationally. By 1956, his contracting company was one of the ten largest in the United States. In 1956, after falling in love with Florida on a business trip, he sold his contracting company and moved to Miami.

CSA requires phenotypic information on family members in a pedigree. A variety of models with different parameters and assumptions about the nature of the inheritance of the trait are fit to the data. CSA studies may include non-genetic models which assume the trait has no genetic component and is only determined by environmental factors, models which include environmental components as well as multi-gene heritability components, and models which include environment, multi-gene heritability, and a single major gene to best fit the data. CSA software uses a maximum likelihood estimator to assign the best fitting coefficients to each component in all models.

The feedback in the oscillator will make the white noise and flicker noise of the feedback amplifier and crystal become the power-law noises of f^{-2} white frequency noise and f^{-3} flicker frequency noise respectively. These noise forms have the effect that the standard variance estimator does not converge when processing time-error samples. This mechanics of the feedback oscillators was unknown when the work on oscillator stability started, but was presented by Leeson at the same time as the set of statistical tools was made available by David W. Allan. For a more thorough presentation on the Leeson effect, see modern phase-noise literature.

Although the term well-behaved statistic often seems to be used in the scientific literature in somewhat the same way as is well-behaved in mathematics (that is, to mean "non-pathological") it can also be assigned precise mathematical meaning, and in more than one way. In the former case, the meaning of this term will vary from context to context. In the latter case, the mathematical conditions can be used to derive classes of combinations of distributions with statistics which are well-behaved in each sense. First Definition: The variance of a well-behaved statistical estimator is finite and one condition on its mean is that it is differentiable in the parameter being estimated.

The local average treatment effect (LATE), also known as the complier average causal effect (CACE), was first introduced into the econometrics literature by Guido W. Imbens and Joshua D. Angrist in 1994. It is the treatment effect for the subset of the sample that takes the treatment if and only if they were assigned to the treatment, otherwise known as the compliers. It is not to be confused with the average treatment effect (ATE), which is the average subject-level treatment effect; the LATE is only the ATE among the compliers. The LATE can be estimated by a ratio of the estimated intent-to-treat effect and the estimated proportion of compliers, or alternatively through an instrumental variable estimator.

53, No. 2, 2006 humanoid robot,K. Ohno and F. Nagashima, "Signal processor," Publication No.~WO2006064571, 2006 GPS,K. Ohno and S. Mori, "A GPS receiver," Domestic Patent, Publication No.~2005-221331, 2005 spatial information system,Nagata, S. Mori, K. Ohno and Y. Hirokawa, "Server system, user terminal, service providing method and service providing system using the server system and the user terminal," United States Patent, Publication No.~20060031410, 2006 etc. During this term, he was with the University of California at Berkeley as visiting fellow to continue to work on the fundamental research on control engineering.K. Ohno, R. Horowitz, “A Variable Structure Multi-rate State Estimator for Seeking Control of HDDs,” IEEE Trans.

The existence of heteroscedasticity is a major concern in regression analysis and the analysis of variance, as it invalidates statistical tests of significance that assume that the modelling errors all have the same variance. While the ordinary least squares estimator is still unbiased in the presence of heteroscedasticity, it is inefficient and generalized least squares should be used instead. Because heteroscedasticity concerns expectations of the second moment of the errors, its presence is referred to as misspecification of the second order. The econometrician Robert Engle won the 2003 Nobel Memorial Prize for Economics for his studies on regression analysis in the presence of heteroscedasticity, which led to his formulation of the autoregressive conditional heteroscedasticity (ARCH) modeling technique.

Biased standard errors lead to biased inference, so results of hypothesis tests are possibly wrong. For example, if OLS is performed on a heteroscedastic data set, yielding biased standard error estimation, a researcher might fail to reject a null hypothesis at a given significance level, when that null hypothesis was actually uncharacteristic of the actual population (making a type II error). Under certain assumptions, the OLS estimator has a normal asymptotic distribution when properly normalized and centered (even when the data does not come from a normal distribution). This result is used to justify using a normal distribution, or a chi square distribution (depending on how the test statistic is calculated), when conducting a hypothesis test.

Whilst there he heard, from the head chef, of a job opening as an apprentice estimator on the Youth Training Scheme at Midas Construction. He did not qualify for the position but was taken on as a tea boy, turning down a position as a radio operator with the Royal Navy to do so; having had experience of unskilled work he worked "like a maniac" to pass his exams and gain qualifications. Fitzgerald attended a building studies course at South Devon College between 1982 and 1986. In 1992, at the age of 28, the head of Midas Construction, Len Lewis, asked Fitzgerald to set up a housebuilding division at the firm and take a 15% stake in it.

Adults 20 years and older should have the cholesterol checked every four to six years. Serum level of Low Density Lipoproteins (LDL) cholesterol, High Density Lipoproteins (HDL) Cholesterol, and triglycerides are commonly tested in primary care setting using a lipid panel. Quantitative levels of lipoproteins and triglycerides contribute toward cardiovascular disease risk stratification via models/calculators such as Framingham Risk Score, ACC/AHA Atherosclerotic Cardiovascular Disease Risk Estimator, and/or Reynolds Risk Scores. These models/calculators may also take into account of family history (heart disease and/or high blood cholesterol), age, gender, Body-Mass-Index, medical history (diabetes, high cholesterol, heart disease), high sensitivity CRP levels, coronary artery calcium score, and ankle-brachial index.

Suppose we are to estimate three unrelated parameters, such as the US wheat yield for 1993, the number of spectators at the Wimbledon tennis tournament in 2001, and the weight of a randomly chosen candy bar from the supermarket. Suppose we have independent Gaussian measurements of each of these quantities. Stein's example now tells us that we can get a better estimate (on average) for the vector of three parameters by simultaneously using the three unrelated measurements. At first sight it appears that somehow we get a better estimator for US wheat yield by measuring some other unrelated statistics such as the number of spectators at Wimbledon and the weight of a candy bar.

In statistics, the interdecile range is the difference between the first and the ninth deciles (10% and 90%). The interdecile range is a measure of statistical dispersion of the values in a set of data, similar to the range and the interquartile range, and can be computed from the (non-parametric) seven-number summary. Despite its simplicity, the interdecile range of a sample drawn from a normal distribution can be divided by 2.56 to give a reasonably efficient estimator of the standard deviation of a normal distribution. This is derived from the fact that the lower (respectively upper) decile of a normal distribution with arbitrary variance is equal to the mean minus (respectively, plus) 1.28 times the standard deviation.

Santos Silva and Tenreyro (2006) did not explain where their result came from and even failed to realize their results were highly anomalous. Martin and Pham (2008) argued that using PPML on gravity severely biases estimates when zero trade flows are frequent. However, their results were challenged by Santos Silva and Tenreyro (2011), who argued that the simulation results of Martin and Pham (2008) are based on misspecified models and showed that the PPML estimator performs well even when the proportions of zeros is very large. In applied work, the model is often extended by including variables to account for language relationships, tariffs, contiguity, access to sea, colonial history, and exchange rate regimes.

Bundle adjustment is almost always used as the last step of every feature-based 3D reconstruction algorithm. It amounts to an optimization problem on the 3D structure and viewing parameters (i.e., camera pose and possibly intrinsic calibration and radial distortion), to obtain a reconstruction which is optimal under certain assumptions regarding the noise pertaining to the observed image features: If the image error is zero-mean Gaussian, then bundle adjustment is the Maximum Likelihood Estimator. Its name refers to the bundles of light rays originating from each 3D feature and converging on each camera's optical center, which are adjusted optimally with respect to both the structure and viewing parameters (similarity in meaning to categorical bundle seems a pure coincidence).

The basic idea of kriging is to predict the value of a function at a given point by computing a weighted average of the known values of the function in the neighborhood of the point. The method is mathematically closely related to regression analysis. Both theories derive a best linear unbiased estimator, based on assumptions on covariances, make use of Gauss–Markov theorem to prove independence of the estimate and error, and make use of very similar formulae. Even so, they are useful in different frameworks: kriging is made for estimation of a single realization of a random field, while regression models are based on multiple observations of a multivariate data set.

In mathematics, the Runge–Kutta–Fehlberg method (or Fehlberg method) is an algorithm in numerical analysis for the numerical solution of ordinary differential equations. It was developed by the German mathematician Erwin Fehlberg and is based on the large class of Runge–Kutta methods. The novelty of Fehlberg's method is that it is an embedded method from the Runge–Kutta family, meaning that identical function evaluations are used in conjunction with each other to create methods of varying order and similar error constants. The method presented in Fehlberg's 1969 paper has been dubbed the RKF45 method, and is a method of order O(h4) with an error estimator of order O(h5).

Linear least squares problems are convex and have a closed-form solution that is unique, provided that the number of data points used for fitting equals or exceeds the number of unknown parameters, except in special degenerate situations. In contrast, non-linear least squares problems generally must be solved by an iterative procedure, and the problems can be non-convex with multiple optima for the objective function. If prior distributions are available, then even an underdetermined system can be solved using the Bayesian MMSE estimator. In statistics, linear least squares problems correspond to a particularly important type of statistical model called linear regression which arises as a particular form of regression analysis.

In statistics and econometrics, the probability framework above still holds, but attention shifts to estimating the parameters of a distribution based on observed data, or testing hypotheses about them. In frequentist estimation parameters are considered "fixed but unknown", whereas in Bayesian estimation they are treated as random variables, and their uncertainty is described as a distribution. In estimation theory of statistics, "statistic" or estimator refers to samples, whereas "parameter" or estimand refers to populations, where the samples are taken from. A statistic is a numerical characteristic of a sample that can be used as an estimate of the corresponding parameter, the numerical characteristic of the population from which the sample was drawn.

The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed. The RMSD represents the square root of the second sample moment of the differences between predicted values and observed values or the quadratic mean of these differences. These deviations are called residuals when the calculations are performed over the data sample that was used for estimation and are called errors (or prediction errors) when computed out-of-sample. The RMSD serves to aggregate the magnitudes of the errors in predictions for various times into a single measure of predictive power.

In non-parametric statistics, the theory of U-statistics is used to establish for statistical procedures (such as estimators and tests) and estimators relating to the asymptotic normality and to the variance (in finite samples) of such quantities.Sen (1992) The theory has been used to study more general statistics as well as stochastic processes, such as random graphs.Page 508 in Pages 381–382 in Page xii in Suppose that a problem involves independent and identically-distributed random variables and that estimation of a certain parameter is required. Suppose that a simple unbiased estimate can be constructed based on only a few observations: this defines the basic estimator based on a given number of observations.

Then he used these theorems to give rigorous proofs of theorems proven by Fisher and Hotelling related to Fisher's maximum likelihood estimator for estimating a parameter of a distribution. After writing a series of papers on the foundations of probability and stochastic processes including martingales, Markov processes, and stationary processes, Doob realized that there was a real need for a book showing what is known about the various types of stochastic processes, so he wrote the book Stochastic Processes.Doob J.L., Stochastic Processes It was published in 1953 and soon became one of the most influential books in the development of modern probability theory. Beyond this book, Doob is best known for his work on martingales and probabilistic potential theory.

The clearest case is where precision is taken to be mean squared error, say r_j = b_j^2 + \tau_j^2 in terms of squared bias and variance for the estimator associated with model j . FIC formulae are then available in a variety of situations, both for handling parametric, semiparametric and nonparametric situations, involving separate estimation of squared bias and variance, leading to estimated precision \hat r_j . In the end the FIC selects the model with smallest estimated mean squared error. Associated with the use of the FIC for selecting a good model is the FIC plot, designed to give a clear and informative picture of all estimates, across all candidate models, and their merit.

During the years of his attendance at the Liceo, he came in contact with the avant-garde world of contemporary art, thanks to his acquaintance with sculptors, Sandro Cherchi and Franco Garelli. He frequented the USIS Library in Turin, and in 1958 he went to the PAC in Milan, to see the exhibition of American painting; a visit which marked the beginning of his interest in Gorky and particularly in abstract expressionism. In 1958 he was admitted to the annual Promotrice delle Belle Arti in Turin. He completed his diploma at the Liceo and then, for a few years, worked as a cost estimator in his father's firm, which specialised in metal structural work.

Collocation is a procedure used in remote sensing to match measurements from two or more different instruments. This is done for two main reasons: for validation purposes when comparing measurements of the same variable, and to relate measurements of two different variables either for performing retrievals or for prediction. In the second case the data is later fed into some type of statistical inverse method such as an artificial neural network, statistical classification algorithm, kernel estimator or a linear least squares. In principle, most collocation problems can be solved by a nearest neighbor search, but in practice there are many other considerations involved and the best method is highly specific to the particular matching of instruments.

The log wind profile is generally considered to be a more reliable estimator of mean wind speed than the wind profile power law in the lowest 10–20 m of the planetary boundary layer. Between 20 m and 100 m both methods can produce reasonable predictions of mean wind speed in neutral atmospheric conditions. From 100 m to near the top of the atmospheric boundary layer the power law produces more accurate predictions of mean wind speed (assuming neutral atmospheric conditions). The neutral atmospheric stability assumption discussed above is reasonable when the hourly mean wind speed at a height of 10 m exceeds 10 m/s where turbulent mixing overpowers atmospheric instability.

Boxplot (with an interquartile range) and a probability density function (pdf) of a Normal Population In descriptive statistics, the interquartile range (IQR), also called the midspread, middle 50%, or Hspread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q3 − Q1. In other words, the IQR is the first quartile subtracted from the third quartile; these quartiles can be clearly seen on a box plot on the data. It is a trimmed estimator, defined as the 25% trimmed range, and is a commonly used robust measure of scale. The IQR is a measure of variability, based on dividing a data set into quartiles.

Quenouille invented this method with the intention of reducing the bias of the sample estimate. Tukey extended this method by assuming that if the replicates could be considered identically and independently distributed, then an estimate of the variance of the sample parameter could be made and that it would be approximately distributed as a t variate with n−1 degrees of freedom (n being the sample size). The basic idea behind the jackknife variance estimator lies in systematically recomputing the statistic estimate, leaving out one or more observations at a time from the sample set. From this new set of replicates of the statistic, an estimate for the bias and an estimate for the variance of the statistic can be calculated.

Malcolm D. Shuster (31 July 1943 – 23 February 2012) was an American physicist and aerospace engineer, whose work contributed significantly to spacecraft attitude determination. In 1977 he joined the Attitude Systems Operation of the Computer Sciences Corporation in Silver Spring, Maryland, during which time he developed the QUaternion ESTimator (QUEST) algorithm for static attitude determination. He later, with F. Landis Markley, helped to develop the standard implementation of the Kalman filter used in spacecraft attitude estimation. During his career, he authored roughly fifty technical papers on subjects in physics and spacecraft engineering, many of which have become seminal within the field of attitude estimation, and held teaching assignments at Johns Hopkins University, Howard University, Carnegie-Mellon University and Tel-Aviv University.

Nonparametric estimation from incomplete observations :Author: Kaplan, EL and Meier, P :Publication data: 1958, Journal of the American Statistical Association, volume 53, pages 457-481. :Description: First description of the now ubiquitous Kaplan-Meier estimator of survival functions from data with censored observations :Importance: Breakthrough, Influence A generalized Wilcoxon test for comparing arbitrarily singly-censored samples :Author: Gehan, EA :Publication data: 1965, Biometrika, volume 52, pages 203-223. :Description: First presentation of the extension of the Wilcoxon rank-sum test to censored data :Importance: Influence Evaluation of survival data and two new rank order statistics arising in its consideration :Author: Mantel, N :Publication data: 1966, Cancer Chemotherapy Reports, volume 50, pages 163-170. :Description: Development of the logrank test for censored survival data.

While this test contributes to damage at the cable site, it is practical because the faulted location would have to be re- insulated when found in any case.Edward J. Tyler, 2005 National Electrical Estimator , Craftsman Book Company, 2004 page 90 In a high resistance grounded distribution system, a feeder may develop a fault to ground but the system continues in operation. The faulted, but energized, feeder can be found with a ring-type current transformer collecting all the phase wires of the circuit; only the circuit containing a fault to ground will show a net unbalanced current. To make the ground fault current easier to detect, the grounding resistor of the system may be switched between two values so that the fault current pulses.

Parsimony is an important exception to this paradigm: though it has been shown that there are circumstances under which it is the maximum likelihood estimator, at its core, it is simply based on the heuristic that changes in character state are rare, without attempting to quantify that rarity. There are three different classes of method for ancestral reconstruction. In chronological order of discovery, these are maximum parsimony, maximum likelihood, and Bayesian Inference. Maximum parsimony considers all evolutionary events equally likely; maximum likelihood accounts for the differing likelihood of certain classes of event; and Bayeisan inference relates the conditional probability of an event to the likelihood of the tree, as well as the amount of uncertainty that is associated with that tree.

From 1950 to 1996, all the publications on particle filters, genetic algorithms, including the pruning and resample Monte Carlo methods introduced in computational physics and molecular chemistry, present natural and heuristic-like algorithms applied to different situations without a single proof of their consistency, nor a discussion on the bias of the estimates and on genealogical and ancestral tree based algorithms. The mathematical foundations and the first rigorous analysis of these particle algorithms are due to Pierre Del Moral in 1996. The article also contains a proof of the unbiased properties of a particle approximations of likelihood functions and unnormalized conditional probability measures. The unbiased particle estimator of the likelihood functions presented in this article is used today in Bayesian statistical inference.

The equivalence of these two approaches was first shown by S. D. Silvey in 1959, which led to the name Lagrange multiplier test that has become more commonly used, particularly in econometrics, since Breusch and Pagan's much-cited 1980 paper. The main advantage of the score test over the Wald test and likelihood-ratio test is that the score test only requires the computation of the restricted estimator. This makes testing feasible when the unconstrained maximum likelihood estimate is a boundary point in the parameter space. Further, because the score test only requires the estimation of the likelihood function under the null hypothesis, it is less specific than the other two tests about the precise nature of the alternative hypothesis.

Besides the originally proposed CCA, the evaluation steps known from partial least squares structural equation modeling (PLS-SEM) are dubbed CCA. It is emphasized that PLS-SEM's evaluation steps, in the following called PLS-CCA, differ from CCA in many regards:. (i) While PLS-CCA aims at conforming reflective and formative measurement models, CCA aims at assessing composite models; (ii) PLS-CCA omits overall model fit assessment, which is a crucial step in CCA as well as SEM; (iii) PLS-CCA is strongly linked to PLS- PM, while for CCA PLS-PM can be employed as one estimator, but this is in no way mandatory. Hence, researchers who employ need to be aware to which technique they are referring to.

The term MMSE more specifically refers to estimation in a Bayesian setting with quadratic cost function. The basic idea behind the Bayesian approach to estimation stems from practical situations where we often have some prior information about the parameter to be estimated. For instance, we may have prior information about the range that the parameter can assume; or we may have an old estimate of the parameter that we want to modify when a new observation is made available; or the statistics of an actual random signal such as speech. This is in contrast to the non-Bayesian approach like minimum- variance unbiased estimator (MVUE) where absolutely nothing is assumed to be known about the parameter in advance and which does not account for such situations.

Note that some of these (such as median, or mid-range) are measures of central tendency, and are used as estimators for a location parameter, such as the mean of a normal distribution, while others (such as range or trimmed range) are measures of statistical dispersion, and are used as estimators of a scale parameter, such as the standard deviation of a normal distribution. L-estimators can also measure the shape of a distribution, beyond location and scale. For example, the midhinge minus the median is a 3-term L-estimator that measures the skewness, and other differences of midsummaries give measures of asymmetry at different points in the tail. Sample L-moments are L-estimators for the population L-moment, and have rather complex expressions.

In practical use in robust statistics, L-estimators have been replaced by M-estimators, which provide robust statistics that also have high relative efficiency, at the cost of being much more computationally complex and opaque. However, the simplicity of L-estimators means that they are easily interpreted and visualized, and makes them suited for descriptive statistics and statistics education; many can even be computed mentally from a five- number summary or seven-number summary, or visualized from a box plot. L-estimators play a fundamental role in many approaches to non-parametric statistics. Though non-parametric, L-estimators are frequently used for parameter estimation, as indicated by the name, though they must often be adjusted to yield an unbiased consistent estimator.

Unlike its linear counterpart, the extended Kalman filter in general is not an optimal estimator (it is optimal if the measurement and the state transition model are both linear, as in that case the extended Kalman filter is identical to the regular one). In addition, if the initial estimate of the state is wrong, or if the process is modeled incorrectly, the filter may quickly diverge, owing to its linearization. Another problem with the extended Kalman filter is that the estimated covariance matrix tends to underestimate the true covariance matrix and therefore risks becoming inconsistent in the statistical sense without the addition of "stabilising noise" . Having stated this, the extended Kalman filter can give reasonable performance, and is arguably the de facto standard in navigation systems and GPS.

Both systems have the same state dimension. A deeper statement of the separation principle is that the LQG controller is still optimal in a wider class of possibly nonlinear controllers. That is, utilizing a nonlinear control scheme will not improve the expected value of the cost functional. This version of the separation principle is a special case of the separation principle of stochastic control which states that even when the process and output noise sources are possibly non-Gaussian martingales, as long as the system dynamics are linear, the optimal control separates into an optimal state estimator (which may no longer be a Kalman filter) and an LQR regulator.. In the classical LQG setting, implementation of the LQG controller may be problematic when the dimension of the system state is large.

Usually some specific distribution assumption on the error term is imposed, such that the parameter \beta is estimated parametrically. For instance, if the distribution of error term is assumed to be normal, then the model is just a multinomial probit model; if it is assumed to be a Gumbel distribution, then the model becomes a multinomial logit model. The parametric model For a concrete example, refer to: Tetsuo Yai, Seiji Iwakura, Shigeru Morichi, Multinomial probit with structured covariance for route choice behavior, Transportation Research Part B: Methodological, Volume 31, Issue 3, June 1997, Pages 195-207, ISSN 0191-2615 is convenient for computation but might not be consistent once the distribution of the error term is misspecified.Jin Yan (2012), "A Smoothed Maximum Score Estimator for Multinomial Discrete Choice Models", Working Paper.

As a consequence, the family of Eleonora de Fonseca Pimentel, who had escaped from Portugal and Rome, moved to Naples to be free from religious persecution. The rich collection of items, collected during the second half of the 19th century by Placido de Sangro, duke of Martina and given to the city of Naples in 1911 by his grandson, the earl of Marsi Placido de Sangro, well reflects the climate of enthusiasm and of renewed interest in the so-called minor arts, which spread over Europe at that time. The duke of Martina, estimator and connoisseur of every type of artefacts, bought items from the main European cities gathering, starting from the second half of the 19th century, an impressive collection of chinaware, majolica and minor artistic artefacts made of glass, leather, coral and ivory.

For these reasons, IV methods invoke implicit assumptions on behavioral response, or more generally assumptions over the correlation between the response to treatment and propensity to receive treatment. The standard IV estimator can recover local average treatment effects (LATE) rather than average treatment effects (ATE). Imbens and Angrist (1994) demonstrate that the linear IV estimate can be interpreted under weak conditions as a weighted average of local average treatment effects, where the weights depend on the elasticity of the endogenous regressor to changes in the instrumental variables. Roughly, that means that the effect of a variable is only revealed for the subpopulations affected by the observed changes in the instruments, and that subpopulations which respond most to changes in the instruments will have the largest effects on the magnitude of the IV estimate.

This reduces the external validity problem to an exercise in graph theory, and has led some philosophers to conclude that the problem is now solved. An important variant of the external validity problem deals with selection bias, also known as sampling bias—that is, bias created when studies are conducted on non- representative samples of the intended population. For example, if a clinical trial is conducted on college students, an investigator may wish to know whether the results generalize to the entire population, where attributes such as age, education, and income differ substantially from those of a typical student. The graph-based method of Bareinboim and Pearl identifies conditions under which sample selection bias can be circumvented and, when these conditions are met, the method constructs an unbiased estimator of the average causal effect in the entire population.

The proportionator adjusts the sampling scheme to select samples that are likely to provide estimates that have a smaller difference. Thus the variance of the estimator is addressed without changing the workload. That results in a gain in efficiency due to the reduction in variance for a given cost. The main steps in sampling biological tissue are: # Selection of a set of animals # Selection of tissue, usually organs from the animals in step 1 # Sampling of the organs by means such as slabbing, cutting bars from organs in step 2 # Selecting a sample of the slices produced from the material in step 3 # Selection of sampling sites on slices from step 4 # Sampling in an optical dissector within the sampling sites chosen in step 5 The typical attempt at increasing efficiency is the counting which occurs in step 6.

Halbert Lynn White Jr. (November 19, 1950 – March 31, 2012) was the Chancellor’s Associates Distinguished Professor of Economics at the University of California, San Diego, and a Fellow of the Econometric Society and the American Academy of Arts and Sciences. A native of Kansas City, Missouri, White graduated salutatorian from Southwest High School in 1968.My Journey to UC San Diego He earned his PhD in Economics at the Massachusetts Institute of Technology in 1976, and spent his first years as an assistant professor in the University of Rochester before moving to UCSD in 1979. He was well known in the field of econometrics for his 1980 paper on robust standard errors (which is the most-cited paper in economics since 1970), and for the heteroscedasticity-consistent estimator and the test for heteroskedascity that are named after him.

Wolpert made many contributions to the early work on machine learning. These include the first Bayesian estimator of the entropy of a distribution based on samples of the distribution, disproving formal claims that the "evidence procedure" is equivalent to hierarchical Bayes, a Bayesian alternative to the chi-squared test, a proof that there is no prior for which the bootstrap procedure is Bayes-optimal, and Bayesian extensions of the bias-plus-variance decomposition. Most prominently, he introduced "stacked generalization", a more sophisticated version of cross- validation that uses held-in / held-out partitions of a data set to combine learning algorithms rather than just choose one of them. This work was developed further by Breiman, Smyth, Clarke and many others, and in particular the top two winners of 2009 Netflix competition made extensive use of stacked generalization (rebranded as "blending").

In statistics and machine learning, lasso (least absolute shrinkage and selection operator; also Lasso or LASSO) is a regression analysis method that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the statistical model it produces. It was originally introduced in geophysics literature in 1986, and later independently rediscovered and popularized in 1996 by Robert Tibshirani, who coined the term and provided further insights into the observed performance. Lasso was originally formulated for linear regression models and this simple case reveals a substantial amount about the behavior of the estimator, including its relationship to ridge regression and best subset selection and the connections between lasso coefficient estimates and so-called soft thresholding. It also reveals that (like standard linear regression) the coefficient estimates do not need to be unique if covariates are collinear.

In statistics, the focused information criterion (FIC) is a method for selecting the most appropriate model among a set of competitors for a given data set. Unlike most other model selection strategies, like the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the deviance information criterion (DIC), the FIC does not attempt to assess the overall fit of candidate models but focuses attention directly on the parameter of primary interest with the statistical analysis, say \mu , for which competing models lead to different estimates, say \hat\mu_j for model j . The FIC method consists in first developing an exact or approximate expression for the precision or quality of each estimator, say r_j for \hat\mu_j , and then use data to estimate these precision measures, say \hat r_j . In the end the model with best estimated precision is selected.

The adjusted R2 can be negative, and its value will always be less than or equal to that of R2. Unlike R2, the adjusted R2 increases only when the increase in R2 (due to the inclusion of a new explanatory variable) is more than one would expect to see by chance. If a set of explanatory variables with a predetermined hierarchy of importance are introduced into a regression one at a time, with the adjusted R2 computed each time, the level at which adjusted R2 reaches a maximum, and decreases afterward, would be the regression with the ideal combination of having the best fit without excess/unnecessary terms. Adjusted R2 can be interpreted as an unbiased (or less biased) estimator of the population R2, whereas the observed sample R2 is a positively biased estimate of the population value.

Zippin was born on July 17, 1926 in Albany, New York, United States, the son of Samuel and Jennie (Perkel) Zippin. He received an AB degree magna cum laude in biology and mathematics, from the State University of New York at Albany in 1947. He was a Research Assistant at the Sterling-Winthrop Research Institute in Rensselaer, New York beginning in 1947. He was awarded a Doctor of Science degree in Biostatistics by the Johns Hopkins School of Hygiene and Public Health in Baltimore, Maryland in 1953. His thesis advisor was William G. Cochran a statistician known for Cochran’s theorem, Cochran-Mantel-Haenzel Test and author of standard biostatistical texts: “Experimental Designs” and “Sampling Techniques”. Zippin’s doctoral thesis, An Evaluation of the Removal Method of Estimating Animal Populations became the basis for the Zippin Estimator, and has been used for estimating populations of a wide variety of animal species.

Such algorithms compute estimates of the likely distribution of annihilation events that led to the measured data, based on statistical principle, often providing better noise profiles and resistance to the streak artifacts common with FBP. Since the density of radioactive tracer is a function in a function space, therefore of extremely high-dimensions, methods which regularize the maximum-likelihood solution turning it towards penalized or maximum a-posteriori methods can have significant advantages for low counts. Examples such as Ulf Grenander's Sieve estimator or Bayes penalty methods, or via I.J. Good's roughness method may yield superior performance to expectation-maximization-based methods which involve a Poisson likelihood function only. As another example, it is considered superior when one does not have a large set of projections available, when the projections are not distributed uniformly in angle, or when the projections are sparse or missing at certain orientations.

In fact, it has been shown that the bootstrap percentage, as an estimator of accuracy, is biased, and that this bias results on average in an underestimate of confidence (such that as little as 70% support might really indicate up to 95% confidence). However, the direction of bias cannot be ascertained in individual cases, so assuming that high values bootstrap support indicate even higher confidence is unwarranted. Another means of assessing support is Bremer support, or the decay index which is a parameter of a given data set, rather than an estimate based on pseudoreplicated subsamples, as are the bootstrap and jackknife procedures described above. Bremer support (also known as branch support) is simply the difference in number of steps between the score of the MPT(s), and the score of the most parsimonious tree that does not contain a particular clade (node, branch).

He is interested in the inference of latent variable modelsO Cappé, E Moulines, « On‐line expectation–maximization algorithm for latent data models », Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2009, pp. 593–613 and in particular hidden Markov chains,R Douc, E Moulines, T Rydén, « Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime », The Annals of statistics, 2004, pp. 2254–2304O. Cappé, E. Moulines, T. Ryden, « Inference in Hidden Markov Models », Springer Series in Statistics, 2006 and non-linear state models (non-linear filtering)R Douc, A Garivier, E Moulines, J Olsson, « Sequential Monte Carlo smoothing for general state space hidden Markov models », The Annals of Applied Probability, 2011, pp. 2109–2145R Douc, E Moulines, D Stoffer, « Nonlinear time series: Theory, methods and applications with R examples », Chapman and Hall/CRC, 2014 In particular, it contributes to filtering methods using interacting particle systems.

When no truncation or censoring occurs, the Kaplan–Meier curve is the complement of the empirical distribution function. In medical statistics, a typical application might involve grouping patients into categories, for instance, those with Gene A profile and those with Gene B profile. In the graph, patients with Gene B die much quicker than those with Gene A. After two years, about 80% of the Gene A patients survive, but less than half of patients with Gene B. To generate a Kaplan–Meier estimator, at least two pieces of data are required for each patient (or each subject): the status at last observation (event occurrence or right-censored), and the time to event (or time to censoring). If the survival functions between two or more groups are to be compared, then a third piece of data is required: the group assignment of each subject.

Braithwaite approach to evaluating the reliability of eyewitness identifications. Wells' testimony in court cases and eyewitness research on system and estimator variables has influenced legislation and state Supreme Court decisions. States such as New Jersey, North Carolina, Ohio, Vermont, Illinois, and Connecticut, for example, now require double-blind lineups and other safeguards for eyewitness identification evidence that Wells advocated. Wells’s work with the U.S. Department of Justice under Attorney General Janet Reno resulted in the first set of national recommendations for law enforcement regarding the collection and preservation of eyewitness evidence (Eyewitness Evidence: A Guide for Law Enforcement). In 2003, the United States Court of Appeals 7th Circuit upheld Wells’ testimony in a Chicago civil suit pertaining to lineup procedures in which the defendant was pardoned innocence after the allegation that the police officer induced the three witnesses to identify him as the perpetrator (Newsome vs.

Robert "Bob" Phillips (August 5, 1939 – April 11, 2016) worked for 40 years in construction, including positions as a bid estimator for Utah contracting companies Jack B. Parsons Construction, and Whitaker Construction. He often told people that his best-known construction job was “the only thing I ever built that ... was to look at and had no purpose.” Phillips was an expert at construction materials and techniques and was proficient in projecting the cost and effort required for a projected job. Phillips was uneasy about using earth-moving equipment in the muck around Rozel Point, where Smithson wanted to create the jetty. “It’s tricky working out on that lake,” Phillips said. “There’s lots of backhoes buried out there.” Smithson, in hip-wader boots, was in full command on the site. “When we got out there, he just took over,” Phillips said. “I don’t think he had done any geology work or anything on it.

In statistics, the score test assesses constraints on statistical parameters based on the gradient of the likelihood function—known as the score—evaluated at the hypothesized parameter value under the null hypothesis. Intuitively, if the restricted estimator is near the maximum of the likelihood function, the score should not differ from zero by more than sampling error. While the finite sample distributions of score tests are generally unknown, it has an asymptotic χ2-distribution under the null hypothesis as first proved by C. R. Rao in 1948, a fact that can be used to determine statistical significance. Since function maximization subject to equality constraints is most conveniently done using a Lagrangean expression of the problem, the score test can be equivalently understood as a test of the magnitude of the Lagrange multipliers associated with the constraints where, again, if the constraints are non-binding at the maximum likelihood, the vector of Lagrange multipliers should not differ from zero by more than sampling error.

The C-CPI-U tries to mitigate the substitution bias that is encountered in CPI-W and CPI-U by employing a Tornqvist formula and utilizing expenditure data in adjacent time periods in order to reflect the effect of any substitution that consumers make across item categories in response to changes in relative prices. The new measure, called a "superlative" index, is designed to be a closer approximation to a "cost-of-living" index than the other measures. The use of expenditure data for both a base period and the current period in order to average price change across item categories distinguishes the C-CPI-U from the existing CPI measures, which use only a single expenditure base period to compute the price change over time. In 1999, the BLS introduced a geometric mean estimator for averaging prices within most of the index's item categories in order to approximate the effect of consumers' responses to changes in relative prices within these item categories.

While only mild conditions are required for MAP estimation to be a limiting case of Bayes estimation (under the 0–1 loss function), it is not very representative of Bayesian methods in general. This is because MAP estimates are point estimates, whereas Bayesian methods are characterized by the use of distributions to summarize data and draw inferences: thus, Bayesian methods tend to report the posterior mean or median instead, together with credible intervals. This is both because these estimators are optimal under squared- error and linear-error loss respectively—which are more representative of typical loss functions—and for a continuous posterior distribution there is no loss function which suggests the MAP is the optimal point estimator. In addition, the posterior distribution may often not have a simple analytic form: in this case, the distribution can be simulated using Markov chain Monte Carlo techniques, while optimization to find its mode(s) may be difficult or impossible.

The use of the term "error" as discussed in the sections above is in the sense of a deviation of a value from a hypothetical unobserved value. At least two other uses also occur in statistics, both referring to observable prediction errors: Mean square error or mean squared error (MSE) and root mean square error (RMSE) refer to the amount by which the values predicted by an estimator differ from the quantities being estimated (typically outside the sample from which the model was estimated). Sum of squares of errors (SSE or SSe), typically abbreviated SSE or SSe, refers to the residual sum of squares (the sum of squared residuals) of a regression; this is the sum of the squares of the deviations of the actual values from the predicted values, within the sample used for estimation. This is also called a least squares estimate, where the regression coefficients are chosen such that the sum of the squares is minimal (i.e.

Longrich admitted that the fact that Horner in his histological study could only find Triceratops subadults was suggestive, but offered the alternative explanation that Triceratops differed from its relatives in retaining a relative young bone structure until old age. On the other hand, bone remodelling is not a reliable estimator of maturity, in view of experimental studies demonstrating that differences in the mechanical strain conditions of various bones can significantly alter the rate or degree of such remodelling and may generate the illusion of old bone tissue. Longrich foresaw that Scanella and Horner would respond to his second test of their hypothesis by claiming that its results were caused by individual variation. According to Longrich, the importance of this factor was limited however: e.g. the size difference between ANSP 15192 and YPM 1831 had better been explained by sexual dimorphism, the former possibly being a young adult female, the latter a subadult male.

Onyinah was employed by the State Construction Company as a regional estimator before his call into the full-time ministry of The Church of Pentecost in 1976. His first ministerial station was a district overseer to Wa District from 1976 to 1981 in the Northern Region. Then transferred to Kumasi as district pastor from 1981 to 1984, He served as Ashanti regional head from 1984 to 1986, he left Ghana to London, UK, for further studies from 1986 to 1988. His return to Ghana saw him appointed as the Koforidua regional head from 1988 to 1991, he became the first international missions director for the church from 1991 to 1996, he continued theological studies at London-UK from 1996 to 2002, he was appointed principal to Pentecost Bible College, which subsequently upgraded to Pentecost University College as its first rector from 2002 to 2008 and finally as chairman of The Church of Pentecost-Worldwide from 2008 to 2018.

In statistics, ordinary least squares (OLS) is a type of linear least squares method for estimating the unknown parameters in a linear regression model. OLS chooses the parameters of a linear function of a set of explanatory variables by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the given dataset and those predicted by the linear function. Geometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression surface—the smaller the differences, the better the model fits the data. The resulting estimator can be expressed by a simple formula, especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation.

It displays estimates on the y axis along with FIC scores on the x axis; thus estimates found to the left in the plot are associated with the better models and those found in the middle and to the right stem from models less or not adequate for the purpose of estimating the focus parameter in question. Generally speaking, complex models (with many parameters relative to sample size) tend to lead to estimators with small bias but high variance; more parsimonious models (with fewer parameters) typically yield estimators with larger bias but smaller variance. The FIC method balances the two desired data of having small bias and small variance in an optimal fashion. The main difficulty lies with the bias b_j , as it involves the distance from the expected value of the estimator to the true underlying quantity to be estimated, and the true data generating mechanism may lie outside each of the candidate models.

He married Elizabeth Ineson of Lancaster, Lancashire England and they subsequently had three children, Linda, Ross and Terry after returning home to Canada where he was educated at the University of Manitoba, and later worked as a journeyman carpenter and car repair estimator for the C.P.R. He was a member of the Winnipeg School Board No.1 from 1962 to 1970, and was also involved in Jubilee Lodge #6 of the Carmen's Union and the Weston Shops ex- Servicemen's Association; the Royal Canadian Legion and the Red River Co- operative movement. He was active in the Cooperative Commonwealth Federation and the New Democratic Party, and often spoke of J.S. Woodsworth and Tommy Douglas as his ideological mentors. He was elected to the Manitoba legislature in the provincial election of 1969, scoring an easy victory in the Winnipeg riding of Logan. He was re-elected in the 1973 election and the 1977 election.

A disaster-related death certificate is issued when a death is not directly caused by a tragedy, but by "fatigue or the aggravation of a chronic disease due to the disaster". According to a June 2012 Stanford University study by John Ten Hoeve and Mark Z. Jacobson, based on linear no-threshold (LNT) model, the radioactivity released could cause 130 deaths from cancer (the lower bound for the estimator being 15 and the upper bound 1100) and 180 cancer cases (the lower bound being 24 and the upper bound 1800), mostly in Japan. Radiation exposure to workers at the plant was projected to result in 2 to 12 deaths. The radioactivity released was an order of magnitude lower than that released from Chernobyl, and some 80% of the radioactivity from Fukushima was deposited over the Pacific Ocean; preventive actions taken by the Japanese government may have substantially reduced the health impact of the radioactivity release. An additional approximately 600 deaths have been reported due to non-radiological causes such as mandatory evacuations.

Tomb of Cardinal Willem van Enckevoirt at Santa Maria dell'Anima in Rome Born around the end of the fifteenth century by Francesco, a native of Caravaggio in Lombardy, according to Giorgio Vasari he studied under sculptor and architect Andrea Ferrucci from Fiesole.Ghisetti Giavarina (2007) In Rome, where he lived in a palace in via delle Coppelle, between Sant'Agostino and palazzo Baldassini, at the beginning of his career had several assignments; from 1527 to 1532 he was superintendent to the spring of S. Peter; until 1541, he was curator of the gold-leaf ceiling of the Basilica of Santa Maria Maggiore; since 1528 and until his death, he was architect of the apostolic Chamber. Moreover, during his whole career he worked also as building estimator. In 1534 started his collaboration with Antonio da Sangallo the Younger: together they prepared apparati effimeri in wood to celebrate the crowning of Pope Paul III (r. 1534-49) and in 1536, the visit to Rome of Holy Roman Emperor Charles V. In 1537 Mangone modified the monastery of the Servites near the Church of San Marcello al Corso, which he completed.