Minimax estimation of the mean matrix of the matrix-variate normal distribution
Autor
Saralees Nadarajah
S. Zinodiny
S. Rezaei
Słowa kluczowe:
Empirical Bayes estimation, matrix-variate normal distribution, mean matrix, minimax estimation
Abstrakt
<p style="text-align: justify;">In this paper, the problem of estimating the mean matrix Θ of a matrix-variate normal distribution with the covariance matrix <em>V I<sub>m</sub></em> is considered under the loss functions,<br /> <em>ω trδ-X'Qδ-X+1-ωtrδ-Θ'Qδ-Θ and k[1-e<sup>-trδ-Θ'Γ^-1δ-Θ</sup>]. </em>We construct a class of empirical Bayes estimators which are better than the maximum likelihood estimator under the first loss function for <em>m > p + 1 </em>and hence show that the maximum likelihood estimator is inadmissible. For the case<em> Q = V = Ip</em>, 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 <em>m > p + 1</em> and hence show that the maximum likelihood estimator is inadmissible.</p>
