http://dx.doi.org/10.1006/jmva.1998.1803

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Title

Nonparametric empirical Bayes estimation of the matrix parameter of the Wishart distribution

Authors

Authors

M. Pensky

Comments

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Abbreviated Journal Title

J. Multivar. Anal.

Keywords

empirical Bayes estimation; Wishart distribution; COVARIANCE-MATRIX; MINIMAX ESTIMATORS; Statistics & Probability

Abstract

We consider independent pairs (X-1, Sigma(1)), (X-2, Sigma(2)), ..., (X-n, Sigma(n)), where each Sigma(i) is distributed according to some unknown density function g(Sigma) and, given Sigma(i) = Sigma, X-i has conditional density function q(x\Sigma) of the Wishart type. In each pair the first component is observable but the second is not. After the (n+1)th observation Xn+1 is obtained, the objective is to estimate Sigma(n+1) corresponding to Xn+1. This estimator is called the empirical Bayes (EB) estimator of Sigma. An EB estimator of Sigma is constructed without any parametric assumptions on g(Sigma). Its posterior mean square risk is examined, and the estimator is demonstrated to be pointwise asymptotically optimal. (C) 1999 Academic Press. AMS 1991 subject classifications: 62H12, 62C12.

Journal Title

Journal of Multivariate Analysis

Volume

69

Issue/Number

2

Publication Date

1-1-1999

Document Type

Article

Language

English

First Page

242

Last Page

260

WOS Identifier

WOS:000080242200006

ISSN

0047-259X

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