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Bayes minimax estimation of the mean matrix of matrix-variate normal distribution under balanced loss function

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  • Zinodiny, S.
  • Rezaei, S.
  • Nadarajah, S.

Abstract

This note considers the problem of simultaneous estimation of matrix-variate normal mean matrix using a balanced loss function when common variance σ2 is unknown. We first find a class of minimax estimators for this problem and show that the maximum likelihood estimator is inadmissible. We obtain a large class of (proper and generalized) Bayes minimax estimators for the mean matrix.

Suggested Citation

  • Zinodiny, S. & Rezaei, S. & Nadarajah, S., 2017. "Bayes minimax estimation of the mean matrix of matrix-variate normal distribution under balanced loss function," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 110-120.
    • Handle: RePEc:eee:stapro:v:125:y:2017:i:c:p:110-120
    DOI: 10.1016/j.spl.2017.02.003
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    References listed on IDEAS

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    1. Tsukuma, Hisayuki, 2009. "Generalized Bayes minimax estimation of the normal mean matrix with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2296-2304, November.
    2. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
    3. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    4. Tsukuma, Hisayuki, 2008. "Admissibility and minimaxity of Bayes estimators for a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2251-2264, November.
    5. Bilodeau, Martin & Kariya, Takeaki, 1989. "Minimax estimators in the normal MANOVA model," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 260-270, February.
    6. Zinodiny, S. & Rezaei, S. & Nadarajah, S., 2014. "Bayes minimax estimation of the multivariate normal mean vector under balanced loss function," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 96-101.
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