Admissibility and minimaxity of Bayes estimators for a normal mean matrix

Hisayuki Tsukuma

Journal of Multivariate Analysis, 2008, vol. 99, issue 10, 2251-2264

Abstract: In some invariant estimation problems under a group, the Bayes estimator against an invariant prior has equivariance as well. This is useful notably for evaluating the frequentist risk of the Bayes estimator. This paper addresses the problem of estimating a matrix of means in normal distributions relative to quadratic loss. It is shown that a matricial shrinkage Bayes estimator against an orthogonally invariant hierarchical prior is admissible and minimax by means of equivariance. The analytical improvement upon every over-shrinkage equivariant estimator is also considered and this paper justifies the corresponding positive-part estimator preserving the order of the sample singular values.

Keywords: primary; 62C10 secondary; 62C15; 62C20; 62J07 Admissibility Bayes estimation Inadmissibility Isotonic regression Minimaxity Order statistic Quadratic loss Simultaneous estimation Singular value decomposition Shrinkage estimator (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (9)

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