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

• Autorzy: Zinodiny, S. , Rezaei, S. , Nadarajah, S.
• Języki publikacji: EN

Abstrakty

EN

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 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 = I_p, 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.

Słowa kluczowe

EN

empirical Bayes estimation; matrix-variate normal distribution; mean matrix; minimax estimation

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2016
• Tom: Vol. 36, Fasc. 2
• Strony: 187--200
• Opis fizyczny: Bibliogr. 18 poz., wykr.

Twórcy

autor

Zinodiny, S.

• Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran,

autor

Rezaei, S.

• Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran,

autor

Nadarajah, S.

• School of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom,

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).