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

Shokofeh Zinodiny, Sadegh Rezaei, Saralees Nadarajah

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

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References


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DOI: 10.6092/issn.1973-2201/6956