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December, 1986 Minimax Estimators of a Normal Mean Vector for Arbitrary Quadratic Loss and Unknown Covariance Matrix
Leon Jay Gleser
Ann. Statist. 14(4): 1625-1633 (December, 1986). DOI: 10.1214/aos/1176350184

Abstract

The problem of finding classes of estimators which dominate the usual estimator $X$ of the mean vector $\mu$ of a $p$-variate normal distribution $(p \geq 3)$ under general quadratic loss is analytically difficult in cases where the covariance matrix is unknown. Estimators of $\mu$ in this case depend upon $X$ and an independent Wishart matrix $W$. In the present paper, integration-by-parts methods for both the multivariate normal and Wishart distributions are combined to yield unbiased estimates of risk difference (versus $X$) for certain classes of estimators, defined indirectly through a "seed" function $h(X, W)$. An application of this technique produces a new class of minimax estimators of $\mu$.

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Leon Jay Gleser. "Minimax Estimators of a Normal Mean Vector for Arbitrary Quadratic Loss and Unknown Covariance Matrix." Ann. Statist. 14 (4) 1625 - 1633, December, 1986. https://doi.org/10.1214/aos/1176350184

Information

Published: December, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0613.62004
MathSciNet: MR868326
Digital Object Identifier: 10.1214/aos/1176350184

Subjects:
Primary: 62C20
Secondary: 62F11, 62H99, 62J07

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 4 • December, 1986
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