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November, 1973 Proper Bayes Minimax Estimators of the Multivariate Normal Mean Vector for the Case of Common Unknown Variances
William E. Strawderman
Ann. Statist. 1(6): 1189-1194 (November, 1973). DOI: 10.1214/aos/1176342567

Abstract

We investigate the problem of estimating the mean vector $\mathbf{\theta}$ of a multivariate normal distribution with covariance matrix equal to $\sigma^2\mathbf{I}_p, \sigma^2$ unknown, and loss $\|\delta - \mathbf{\theta}\|^2/\sigma^2$. We first find a class of minimax estimators for this problem which enlarges a class given by Baranchik. This result is then used to show that for sufficiently large sample sizes (which never need exceed 4) proper Bayes minimax estimators exist for $\mathbf{\theta}$ if $p \geqq 5$.

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William E. Strawderman. "Proper Bayes Minimax Estimators of the Multivariate Normal Mean Vector for the Case of Common Unknown Variances." Ann. Statist. 1 (6) 1189 - 1194, November, 1973. https://doi.org/10.1214/aos/1176342567

Information

Published: November, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0286.62007
MathSciNet: MR365806
Digital Object Identifier: 10.1214/aos/1176342567

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 6 • November, 1973
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