the Hodges–Lehmann estimator is a consistent and median-unbiased estimate of the population median. For non-symmetric populations, the Hodges–Lehmann estimator...

the Hodges–Lehmann estimator is a robust and highly efficient estimator of the population median; for non-symmetric distributions, the Hodges–Lehmann estimator...

one of the eponyms of the Lehmann–Scheffé theorem and of the Hodges–Lehmann estimator of the median of a population. Lehmann was born in Strasbourg, Alsace-Lorraine...

the Lehmann–Scheffé theorem ties together completeness, sufficiency, uniqueness, and best unbiased estimation. The theorem states that any estimator that...

rest of his career. Hodges is best known for his contributions to the field of statistics, including the Hodges–Lehmann estimator, the nearest neighbor...

delete-1, such as the delete-m jackknife or the delete-all-but-2 Hodges–Lehmann estimator, overcome this problem for the medians and quantiles by relaxing...

minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than...

of quality of an estimator, of an experimental design, or of a hypothesis testing procedure. Essentially, a more efficient estimator needs fewer input...

In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter...

that characterizes the transformation of an arbitrarily crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of...

X_{2})} is sufficient but not complete. It admits a non-zero unbiased estimator of zero, namely X 1 − X 2 {\textstyle X_{1}-X_{2}} . Most parametric models...

The Kaplan–Meier estimator, also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime...

The standard error (SE) of a statistic (usually an estimator of a parameter, like the average or mean) is the standard deviation of its sampling distribution...

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...

Gauss–Markov theorem does not apply. Similar to the Hodges' estimator, the James-Stein estimator is superefficient and non-regular at θ = 0 {\displaystyle...

standard deviation. Such a statistic is called an estimator, and the estimator (or the value of the estimator, namely the estimate) is called a sample standard...

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...

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...

estimator approaches the MAP estimator, provided that the distribution of θ {\displaystyle \theta } is quasi-concave. But generally a MAP estimator is...

have a random sample of n people. The sample mean could serve as a good estimator of the population mean. Then we have: The difference between the height...

deviation ellipse is lower. The derivation of the maximum-likelihood estimator of the covariance matrix of a multivariate normal distribution is straightforward...

can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random...

sufficient and ancillary statistics Lehmann–Scheffé theorem: a complete sufficient estimator is the best estimator of its expectation Rao–Blackwell theorem...

treatments) was quantified using the Hodges–Lehmann (HL) estimator, which is consistent with the Wilcoxon test. This estimator (HLΔ) is the median of all possible...

The ratio estimator is a statistical estimator for the ratio of means of two random variables. Ratio estimates are biased and corrections must be made...

{s}{\bar {x}}}} But this estimator, when applied to a small or moderately sized sample, tends to be too low: it is a biased estimator. For normally distributed...

maximum likelihood estimator (MLE) of the covariance matrix differs from the ordinary least squares (OLS) estimator. MLE estimator:[citation needed] Σ...

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...

the bootstrap. Given a sample of size n {\displaystyle n} , a jackknife estimator can be built by aggregating the parameter estimates from each subsample...

uncorrelated). Let α ^ , β ^ = least-squares estimators , S E α ^ , S E β ^ = the standard errors of least-squares estimators . {\displaystyle {\begin{aligned}{\hat...