MINIMAX ESTIMATION OF THE MEAN MATRIX OF THE
MATRIX-VARIATE NORMAL DISTRIBUTION
S. Zinodiny
S. Rezaei
S. Nadarajah
Abstract: In this paper, the problem of estimating the mean matrix
of a matrix-variate normal distribution with the covariance matrix
is considered under the loss functions,
and . We construct a class of empirical Bayes estimators
which are better than the maximum likelihood estimator under the first loss function for
and hence show that the maximum likelihood estimator is inadmissible. For the
case , 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
for and hence show that the maximum likelihood estimator is inadmissible.
2010 AMS Mathematics Subject Classification: Primary 62C15; Secondary
62C20.
Keywords and phrases: Empirical Bayes estimation, matrix-variate normal distribution,
mean matrix, minimax estimation.