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Minimax Bayes estimators of a multivariate normal mean

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  • Faith, Ray E.

Abstract

In three or more dimensions it is well known that the usual point estimator for the mean of a multivariate normal distribution is minimax but not admissible with respect to squared Euclidean distance loss. This paper gives sufficient conditions on the prior distribution under which the Bayes estimator has strictly lower risk than the usual estimator. Examples are given for which the posterior density is useful in the formation of confidence sets.

Suggested Citation

  • Faith, Ray E., 1978. "Minimax Bayes estimators of a multivariate normal mean," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 372-379, September.
    • Handle: RePEc:eee:jmvana:v:8:y:1978:i:3:p:372-379
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    Citations

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    Cited by:

    1. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2017. "Proper Bayes and minimax predictive densities related to estimation of a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 138-150.
    2. Brani Vidakovic, 1999. "Linear Versus Nonlinear Rules for Mixture Normal Priors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 111-124, March.
    3. Maruyama, Yuzo, 2004. "Stein's idea and minimax admissible estimation of a multivariate normal mean," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 320-334, February.
    4. Maruyama, Yuzo, 1998. "A Unified and Broadened Class of Admissible Minimax Estimators of a Multivariate Normal Mean," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 196-205, February.
    5. 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.
    6. 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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