Accession Number : ADA318636

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

Descriptive Note : Technical rept.,

Corporate Author : PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS

Personal Author(s) : Liang, TaChen

PDF Url : ADA318636

Report Date : MAY 1996

Pagination or Media Count : 36

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.

Descriptors :   *BAYES THEOREM, OPTIMIZATION, STATISTICAL TESTS, PROBABILITY DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, STATISTICAL DATA, ASYMPTOTIC SERIES, CONVERGENCE, HYPOTHESES, EXPONENTIAL FUNCTIONS.

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE