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Hierarchical Empirical Bayes Estimation of Two Sample Means Under Divergence Loss

Abstract

We consider the problem of simultaneous estimation of two population means when one suspects that the two means are nearly equal. It is shown that the hierarchical empirical Bayes estimators which shrink the sample means towards the suspected hypothesis dominate the sample mean vectors in simultaneous estimation under the divergence loss function.

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Acknowledgments

The authors are grateful to the Editor, the Associate Editor and two reviewers for their valuable comments and helpful suggestions. Research of the second author was supported in part by Grant-in-Aid for Scientific Research (15H01943 and 26330036) from Japan Society for the Promotion of Science.

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Correspondence to Malay Ghosh.

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Ghosh, M., Kubokawa, T. Hierarchical Empirical Bayes Estimation of Two Sample Means Under Divergence Loss. Sankhya A 80 (Suppl 1), 70–83 (2018). https://doi.org/10.1007/s13171-018-0155-5

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  • DOI: https://doi.org/10.1007/s13171-018-0155-5

Keywords and phrases

  • Dominance property
  • Hellinger divergence
  • Kullback-Leibler divergence
  • Minimaxity
  • Risk function
  • Shrinkage estimator
  • Simultaneous estimation
  • Stein phenomenon

AMS (2000) subject classification

  • Primary 62C20
  • Secondary 62C12