Minimax estimation of the mean matrix of the matrix-variate normal distribution
Saralees Nadarajah, S. Zinodiny, Sadegh Rezaei · Probability and Mathematical Statistics · 2016
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 trδ-X'Qδ-X+1-ωtrδ-Θ'Qδ-Θ and k[1-e-trδ-Θ'Γ^-1δ-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.]]>