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Generalized Bayes minimax estimation of the normal mean matrix with unknown covariance matrix

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  • Tsukuma, Hisayuki

Abstract

This paper addresses the problem of estimating the normal mean matrix in the case of unknown covariance matrix. This problem is solved by considering generalized Bayesian hierarchical models. The resulting generalized Bayes estimators with respect to an invariant quadratic loss function are shown to be matricial shrinkage equivariant estimators and the conditions for their minimaxity are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2296-2304
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    References listed on IDEAS

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    1. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2007. "Methods for improvement in estimation of a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1592-1610, September.
    2. Konno, Yoshihiko, 1991. "On estimation of a matrix of normal means with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 36(1), pages 44-55, January.
    3. Ghosh, Malay & Shieh, Gwowen, 1991. "Empirical Bayes minimax estimators of matrix normal means," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 306-318, August.
    4. Bilodeau, Martin & Kariya, Takeaki, 1989. "Minimax estimators in the normal MANOVA model," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 260-270, February.
    5. 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.
    6. Zheng, Z., 1986. "Selecting a minimax estimator doing well at a point," Journal of Multivariate Analysis, Elsevier, vol. 19(1), pages 14-23, June.
    7. Zheng, Z., 1986. "On estimation of matrix of normal mean," Journal of Multivariate Analysis, Elsevier, vol. 18(1), pages 70-82, February.
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    Cited by:

    1. Yuasa, Ryota & Kubokawa, Tatsuya, 2023. "Weighted shrinkage estimators of normal mean matrices and dominance properties," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    2. Tsukuma, Hisayuki, 2010. "Shrinkage priors for Bayesian estimation of the mean matrix in an elliptically contoured distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1483-1492, July.
    3. Hoff, Peter D., 2011. "Hierarchical multilinear models for multiway data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 530-543, January.
    4. Mori, Yuichi & Suzuki, Taiji, 2018. "Generalized ridge estimator and model selection criteria in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 243-261.
    5. 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.
    6. Hu, Guikai & Peng, Ping, 2012. "Matrix linear minimax estimators in a general multivariate linear model under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 286-295.
    7. Shokofeh Zinodiny & Saralees Nadarajah, 2024. "A New Class of Bayes Minimax Estimators of the Mean Matrix of a Matrix Variate Normal Distribution," Mathematics, MDPI, vol. 12(7), pages 1-14, April.

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