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Contents of PMS, Vol. 36, Fasc. 2,
pages 187 - 200
 

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 Θ of a matrix-variate normal distribution with the covariance matrix V ⊗ I m is considered under the loss functions, ω tr((δ - X )′Q(δ - X))+ (1- ω)tr((δ - Θ)′Q(δ- Θ )) and - tr((δ-Θ )′Γ -1(δ-Θ)) k [1- e ] . 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.

2010 AMS Mathematics Subject Classification: Primary 62C15; Secondary 62C20.

Keywords and phrases: Empirical Bayes estimation, matrix-variate normal distribution, mean matrix, minimax estimation.

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