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Minimax estimators in the normal MANOVA model

Author

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  • Bilodeau, Martin
  • Kariya, Takeaki

Abstract

This paper considers the problem of estimating the coefficient matrix B: m - p in a normal multivariate regression model under the risk matrix : m - m and obtains classes of minimax estimators for Baranchik type, Strawderman type, Efron-Morris type, and Stein type estimators.

Suggested Citation

  • Bilodeau, Martin & Kariya, Takeaki, 1989. "Minimax estimators in the normal MANOVA model," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 260-270, February.
    • Handle: RePEc:eee:jmvana:v:28:y:1989:i:2:p:260-270
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    Citations

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    Cited by:

    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. Hisayuki Tsukuma & Tatsuya Kubokawa, 2014. "A Unified Approach to Estimating a Normal Mean Matrix in High and Low Dimensions," CIRJE F-Series CIRJE-F-926, CIRJE, Faculty of Economics, University of Tokyo.
    3. Ahmed, S. E. & Krzanowski, W. J., 2004. "Biased estimation in a simple multivariate regression model," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 689-696, May.
    4. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2016. "Unified improvements in estimation of a normal covariance matrix in high and low dimensions," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 233-248.
    5. Srivastava, M. S. & Kubokawa, T., 2005. "Minimax multivariate empirical Bayes estimators under multicollinearity," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 394-416, April.
    6. Kubokawa, T. & Srivastava, M. S., 2002. "Estimating Risk and the Mean Squared Error Matrix in Stein Estimation," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 39-64, July.
    7. Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.
    8. Tatsuya Kubokawa & M. S. Srivastava, 2002. "Minimax Multivariate Empirical Bayes Estimators under Multicollinearity," CIRJE F-Series CIRJE-F-187, CIRJE, Faculty of Economics, University of Tokyo.
    9. Hisayuki Tsukuma & Tatsuya Kubokawa, 2014. "Unified Improvements in Estimation of a Normal Covariance Matrix in High and Low Dimesions," CIRJE F-Series CIRJE-F-937, CIRJE, Faculty of Economics, University of Tokyo.
    10. 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.
    11. Hisayuki Tsukuma & Tatsuya Kubokawa, 2005. "Methods for Improvement in Estimation of a Normal Mean Matrix," CIRJE F-Series CIRJE-F-378, CIRJE, Faculty of Economics, University of Tokyo.
    12. Xu, Kai & He, Daojiang, 2015. "Further results on estimation of covariance matrix," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 11-20.
    13. Imai, Ryo & Kubokawa, Tatsuya & Ghosh, Malay, 2019. "Bayesian simultaneous estimation for means in k-sample problems," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 49-60.
    14. 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.
    15. Oman, Samuel D., 2002. "Minimax Hierarchical Empirical Bayes Estimation in Multivariate Regression," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 285-301, February.
    16. T Matsuda & W E Strawderman, 2022. "Estimation under matrix quadratic loss and matrix superharmonicity [Shrinkage estimation with a matrix loss function]," Biometrika, Biometrika Trust, vol. 109(2), pages 503-519.
    17. 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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