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Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance

Author

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  • Zinodiny, S.
  • Strawderman, W.E.
  • Parsian, A.

Abstract

We investigate the problem of estimating the mean vector [theta] of a multivariate normal distribution with covariance matrix [sigma]2Ip, when [sigma]2 is unknown, and where the loss function is . We find a large class of (proper and generalized) Bayes minimax estimators of [theta], and show that the result of Strawderman (1973) [8] is a special case of our result. Since a large subclass of the estimators found are proper Bayes, and therefore admissible, the class of admissible minimax estimators is substantially enlarged as well.

Suggested Citation

  • Zinodiny, S. & Strawderman, W.E. & Parsian, A., 2011. "Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1256-1262, October.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:9:p:1256-1262
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    References listed on IDEAS

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    1. Fourdrinier, Dominique & Kortbi, Othmane & Strawderman, William E., 2008. "Bayes minimax estimators of the mean of a scale mixture of multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 74-93, January.
    2. Wells, Martin T. & Zhou, Gongfu, 2008. "Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2208-2220, November.
    3. Maruyama, Yuzo, 2003. "Admissible minimax estimators of a mean vector of scale mixtures of multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 274-283, February.
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    Cited by:

    1. 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.
    2. Zinodiny, S. & Rezaei, S. & Arjmand, O. Naghshineh & Nadarajah, S., 2013. "Bayes minimax estimation of the multivariate normal mean vector under quadratic loss functions," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2052-2056.

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