Minimax Estimation of the Mean Matrix of the Matrix Variate Normal Distribution under the Divergence Loss Function

Abstract

The problem of estimating the mean matrix of a matrix-variate normal distribution with a covariance matrix is considered under two loss functions. We construct a class of empirical Bayes estimators which are better than the maximum likelihood estimator under the first loss function and hence show that the maximum likelihood estimator is inadmissible. We find a general class of minimax estimators. Also we give a class of estimators that improve on the maximum likelihood estimator under the second loss function and hence show that the maximum likelihood estimator is inadmissible.

Keywords

• Empirical Bayes estimation
• Matrix variate normal distribution
• Mean matrix
• Minimax estimation