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

    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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