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Minimax estimation of the mean matrix of the matrix-variate normal distribution

Zinodiny S., Rezaei S., Nadarajah S.

Probability and Mathematical Statistics

2016

Vol. 36, Fasc. 2

187--200

In this paper, the problem of estimating the mean matrix Θ of a matrix-variate normal distribution with the covariance matrix V⊗ Im is considered under the loss functions, ω tr((δ − X)′ Q(δ − X)) + (1 − ω) tr((δ − Θ)′ Q(δ − Θ)) and k[1−e−tr((δ − Θ)′ Γ−1(δ − Θ))]. We construct a class of empirical Bayes estimators which are better than the maximum likelihood estimator under the first loss function for m > p + 1 and hence show that the maximum likelihood estimator is inadmissible. For the case Q = V = Ip, 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 m > p + 1 and hence show that the maximum likelihood estimator is inadmissible.