Empirical Bayes Two-Tail Tests in a Discrete Exponential Family.
PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS
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This paper deals with the problem of testing hypotheses Hotheta member of THETA1, THETA2 versus H1theta 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 Oexp-rn for some r0, where n is the number of historical data at hand for the present testing problem.
- Statistics and Probability