Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance

Abstract

We investigate the problem of estimating the mean vector [theta] of a multivariate normal distribution with covariance matrix [sigma]2Ip, when [sigma]2 is unknown, and where the loss function is . We find a large class of (proper and generalized) Bayes minimax estimators of [theta], and show that the result of Strawderman (1973) [8] is a special case of our result. Since a large subclass of the estimators found are proper Bayes, and therefore admissible, the class of admissible minimax estimators is substantially enlarged as well.Bayes estimation Minimax estimation Multivariate normal mean Unknown variance

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