Generalized Bayes Estimators with Closed forms for the Normal Mean and Covariance Matrices

TL;DR

This paper introduces closed-form generalized Bayes estimators for the mean and covariance matrices in multivariate normal models, establishing conditions for their minimaxity and dominance properties under various loss functions.

Contribution

It provides novel closed-form solutions for generalized Bayes estimators of mean and covariance matrices, along with conditions for their optimality and dominance.

Findings

Closed-form estimators for the mean matrix are derived.

Conditions for minimaxity under quadratic loss are established.

Dominance properties of covariance estimators under Stein loss are discussed.

Abstract

In the estimation of the mean matrix in a multivariate normal distribution, the generalized Bayes estimators with closed forms are provided, and the sufficient conditions for their minimaxity are derived relative to both matrix and scalar quadratic loss functions. The generalized Bayes estimators of the covariance matrix are also given with closed forms, and the dominance properties are discussed for the Stein loss function.