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

  1. S. Zinodiny
  2. S. Rezaei
  3. Saralees Nadarajah

Abstract

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.

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Probability and Mathematical Statistics

36, z. 2, 2016

Pages from 187 to 200

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