Linear empirical Bayes estimation in the case of the Wishart distribution

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    Keywords

    empirical Bayes estimation; the Wishart distribution; COVARIANCE-MATRIX; MINIMAX ESTIMATORS; MOMENTS; 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 a 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 an empirical Bayes (EB) estimator of Sigma. We construct a linear EB estimator of Sigma and examine its precision.

    Journal Title

    Communications in Statistics-Theory and Methods

    Volume

    29

    Issue/Number

    8

    Publication Date

    1-1-2000

    Document Type

    Article

    Language

    English

    First Page

    1787

    Last Page

    1799

    WOS Identifier

    WOS:000088283000006

    ISSN

    0361-0926

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