Minimax Estimation of the Mean Matrix of the Matrix Variate Normal Distribution under the Divergence Loss Function
Keywords:Empirical Bayes estimation, Matrix variate normal distribution, Mean matrix, Minimax estimation
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.
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