Open Access
March, 1982 Selecting a Minimax Estimator of a Multivariate Normal Mean
James O. Berger
Ann. Statist. 10(1): 81-92 (March, 1982). DOI: 10.1214/aos/1176345691


The problem of estimating a $p$-variate normal mean under arbitrary quadratic loss when $p \geq 3$ is considered. Any estimator having uniformly smaller risk than the maximum likelihood estimator $\delta^0$ will have significantly smaller risk only in a fairly small region of the parameter space. A relatively simple minimax estimator is developed which allows the user to select the region in which significant improvement over $\delta^0$ is to be achieved. Since the desired region of improvement should probably be chosen to coincide with prior beliefs concerning the whereabouts of the normal mean, the estimator is also analyzed from a Bayesian viewpoint.


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James O. Berger. "Selecting a Minimax Estimator of a Multivariate Normal Mean." Ann. Statist. 10 (1) 81 - 92, March, 1982.


Published: March, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0485.62046
MathSciNet: MR642720
Digital Object Identifier: 10.1214/aos/1176345691

Primary: 62C99
Secondary: 62F10 , 62F15 , 62H99

Keywords: Bayes risk , minimax , normal mean , prior information , quadratic loss , risk function

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 1 • March, 1982
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