Empirical Bayes Two-Tail Tests in a Discrete Exponential Family.

Abstract

This paper deals with the problem of testing hypotheses Ho:theta member of THETA1, THETA2 versus H1:theta not a member of THETA1, THETA2, where 0 < theta1 < theta2 < infinity, for the parameter theta in a discrete exponential family via the empirical Bayes approach. First, the behavior of the Bayes test is examined. Then the empirical Bayes test is constructed by mimicking the behavior of the Bayes test. The asymptotic optimality of the empirical Bayes tests is investigated. It is shown that, under very mild regularity conditions, the proposed empirical Bayes test is asymptotically optimal and its associated Bayes risk converges to the minimum Bayes risk with a rate of convergence of order O(exp(-rn)) for some r>0, where n is the number of historical data at hand for the present testing problem.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1996
Accession Number
ADA318636

Entities

People

  • Tachen Liang

Organizations

  • Purdue University

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DTIC Thesaurus Topics

  • Abstracts
  • Classification
  • Convergence
  • Distribution Functions
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  • Families (Human)
  • Inequalities
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Fields of Study

  • Mathematics

Readers

  • Statistical inference.