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Empirical and hierarchical bayes competitors of preliminary test estimators in two sample problems

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  • Ghosh, Malay
  • Sinha, Bimal K.

Abstract

We consider the problem of estimation of [mu]1 when it is suspected that [mu]1 [approximate] [mu]2 based on independent samples from Np([mu]1, [sigma]2V1) and Np([mu]2, [sigma]2V2). We assume V1, V2 known but [sigma]2 unknown. First, the EB estimator is derived and its Bayesian and frequentist properties are studied. Second, a modified EB estimator is proposed and shown to dominate a preliminary test estimator. Finally, a hierarchical Bayes approach is proposed as an alternative to EB estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:27:y:1988:i:1:p:206-227
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    Cited by:

    1. Malay Ghosh & Tatsuya Kubokawa, 2018. "Hierarchical Empirical Bayes Estimation of Two Sample Means Under Divergence Loss," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 70-83, December.
    2. 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.

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