Minimax estimator

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A statistical estimator obtained as a result of the application of the notion of a minimax statistical procedure in the problem of statistical estimation.

Example 1. Let a random variable be subject to the binomial law with parameters and , where , , is unknown. The statistic

is a minimax estimator for the parameter with respect to the loss function

Example 2. Let be independent random variables subject to the same probability law, with a continuous probability density , , . The Pitman estimator

is a minimax estimator for the unknown shift parameter relative to the loss function , where are the order statistics (cf. Order statistic) obtained from the sample and . In particular, if , then .


[1] S. Zacks, "The theory of statistical inference" , Wiley (1971)
[2] D.R. Cox, D.V. Hinkley, "Theoretical statistics" , Chapman & Hall (1974)
How to Cite This Entry:
Minimax estimator. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article