Empirical Bayes Simultaneous Selection Procedures for Comparing Normal Populations with a Standard,

Abstract

In this paper, we derive statistical selection procedures to partition k normal populations into 'good' or 'bad' ones, respectively, using the nonparametric empirical Bayes approach. The relative regret risk of a selection procedure is used as a measure of its performance. We establish the asymptotic optimality of the proposed empirical Bayes selection procedures and investigate the associated rates of convergence. Under a very mild condition, the proposed empirical Bayes selection procedures are shown to have rates of convergence of order close to O(k(-1/2)) where k is the number of populations involved in the selection problem. With further strong assumptions, the empirical Bayes selection procedures have rates of convergence of order O(k(-a(r-1)/(2r+1))) where 1 <a< 2 and r is an integer greater than 2.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1996
Accession Number
ADA313572

Entities

People

  • Shanti Gupta
  • Tachen Liang

Organizations

  • Purdue University

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  • C4I

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  • Mathematics

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  • Operations Research
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