In statistics, Hodges' estimator (or the Hodges–Le Cam estimator), named for Joseph Hodges, is a famous counterexample of an estimator which is "superefficient"...

and by Joseph Hodges and Erich Lehmann, and so it is also called the "Hodges–Lehmann–Sen estimator". In the simplest case, the "Hodges–Lehmann" statistic...

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

Fix) and Hodges’ estimator. Hodges, Joseph L.; Lehmann, E. L. (1964). Basic concepts of probability and statistics. Holden-Day. Joe Hodges Memorial Joseph...

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

θ {\displaystyle \theta } ). Both the Hodges' estimator and the James-Stein estimator are non-regular estimators when the population parameter θ {\displaystyle...

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...

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

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...

History of randomness History of statistics Hitting time Hodges' estimator Hodges–Lehmann estimator Hoeffding's independence test Hoeffding's lemma Hoeffding's...

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

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

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...

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

estimates. Unfortunately, when there are outliers in the data, classical estimators often have very poor performance, when judged using the breakdown point...

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...

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

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...

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

{X}},} an estimator (estimation rule) δ M {\displaystyle \delta ^{M}\,\!} is called minimax if its maximal risk is minimal among all estimators of θ {\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...

modelling errors all have the same variance. While the ordinary least squares estimator is still unbiased in the presence of heteroscedasticity, it is inefficient...

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...

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

used for estimating a population parameter, the statistic is called an estimator. A population parameter is any characteristic of a population under study...

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...

supervised learning method. It was first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. Most often, it is used for...

uniqueness, and best unbiased estimation. The theorem states that any estimator that is unbiased for a given unknown quantity and that depends on the...

{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...