A study on theory and applications of Bayesian estimation for parameter matrices in multivariate statistical models

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This study addresses the Bayesian estimation problems of parameter matrices in multivariate statistical models which are used for analyses of two dimensional array data. The principal aim of the study is to develop optimal Bayes estimators and shrinkage-type estimators not only from the point of view of statistical decision theory, but also from that of practical application. Some results are obtained for a least favorable sequence of prior distributions in covariance estimation, dominance properties of a generalized Bayes estimator of a bounded precision matrix, inadmissibility of shrinkage estimators for a mean matrix, and others.