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Stein's idea and minimax admissible estimation of a multivariate normal mean

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  • Maruyama, Yuzo

Abstract

We consider estimation of a multivariate normal mean vector under sum of squared error loss.We propose a new class of minimax admissible estimator which are generalized Bayes with respect to a prior distribution which is a mixture of a point prior at the origin and a continuous hierarchical type prior. We also study conditions under which these generalized Bayes minimax estimators improve on the James-Stein estimator and on the positive-part James-Stein estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:2:p:320-334
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    References listed on IDEAS

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    1. Faith, Ray E., 1978. "Minimax Bayes estimators of a multivariate normal mean," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 372-379, September.
    2. 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.
    3. Kubokawa, Tatsuya, 1991. "An approach to improving the James-Stein estimator," Journal of Multivariate Analysis, Elsevier, vol. 36(1), pages 121-126, January.
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    Cited by:

    1. Yuzo Maruyama & William Strawderman, 2005. "Necessary conditions for dominating the James-Stein estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 157-165, March.
    2. Maruyama, Yazo & Takemura, Akimichi, 2008. "Admissibility and minimaxity of generalized Bayes estimators for spherically symmetric family," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 50-73, January.

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