The Annals of Statistics

Proper Bayes Minimax Estimators of the Multivariate Normal Mean Vector for the Case of Common Unknown Variances

William E. Strawderman

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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 $p \geqq 5$.

Article information

Source
Ann. Statist., Volume 1, Number 6 (1973), 1189-1194.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342567

Digital Object Identifier
doi:10.1214/aos/1176342567

Mathematical Reviews number (MathSciNet)
MR365806

Zentralblatt MATH identifier
0286.62007

JSTOR
links.jstor.org

Citation

Strawderman, William E. Proper Bayes Minimax Estimators of the Multivariate Normal Mean Vector for the Case of Common Unknown Variances. Ann. Statist. 1 (1973), no. 6, 1189--1194. doi:10.1214/aos/1176342567. https://projecteuclid.org/euclid.aos/1176342567


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