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Bayesian simultaneous estimation for means in k-sample problems

Author

Listed:
  • Imai, Ryo
  • Kubokawa, Tatsuya
  • Ghosh, Malay

Abstract

This paper is concerned with the simultaneous estimation of k population means when one suspects that the k means are nearly equal. As an alternative to the preliminary test estimator based on the test statistics for testing hypothesis of equal means, we derive Bayesian and minimax estimators which shrink individual sample means toward a pooled mean estimator given under the hypothesis. It is shown that both the preliminary test estimator and the Bayesian minimax shrinkage estimators are further improved by shrinking the pooled mean estimator. The performance of the proposed shrinkage estimators is investigated by simulation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:49-60
    DOI: 10.1016/j.jmva.2018.08.013
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    References listed on IDEAS

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    1. Ghosh, Malay & Sinha, Bimal K., 1988. "Empirical and hierarchical bayes competitors of preliminary test estimators in two sample problems," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 206-227, October.
    2. Perron, F., 1993. "Estimation of a Mean Vector in a Two-Sample Problem," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 254-261, August.
    3. Bilodeau, Martin & Kariya, Takeaki, 1989. "Minimax estimators in the normal MANOVA model," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 260-270, February.
    4. 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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