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May, 1973 A Family of Admissible Minimax Estimators of the Mean of a Multivariate Normal Distribution
Khursheed Alam
Ann. Statist. 1(3): 517-525 (May, 1973). DOI: 10.1214/aos/1176342417

Abstract

Let the $p$-component vector $X$ be normally distributed with mean $\xi$ and covariance $\sigma^2I$ where $I$ denotes the identity matrix and $\sigma$ is known. For estimating $\xi$ with quadratic loss, it is known that $X$ is minimax but inadmissible for $p \geqq 3$. We obtain a family of estimators which dominate $X$ and are admissible. These estimators are, therefore, both minimax and admissible.

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Khursheed Alam. "A Family of Admissible Minimax Estimators of the Mean of a Multivariate Normal Distribution." Ann. Statist. 1 (3) 517 - 525, May, 1973. https://doi.org/10.1214/aos/1176342417

Information

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

zbMATH: 0259.62007
MathSciNet: MR353524
Digital Object Identifier: 10.1214/aos/1176342417

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 3 • May, 1973
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