Hodges' estimator
Type of statistical estimator / From Wikipedia, the free encyclopedia
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In statistics, Hodges' estimator[1] (or the Hodges–Le Cam estimator[2]), named for Joseph Hodges, is a famous counterexample of an estimator which is "superefficient",[3] 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. In general, any superefficient estimator may surpass a regular estimator at most on a set of Lebesgue measure zero.[4]
Although Hodges discovered the estimator he never published it; the first publication was in the doctoral thesis of Lucien Le Cam.[5]