Accession Number : ADA313657

Title :   Selecting Good Exponential Populations Compared with a Control: A Nonparametric Empirical Bayes Approach.

Descriptive Note : Technical rept.,

Corporate Author : PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS

Personal Author(s) : Gupta, Shanti S. ; Liang, TaChen

PDF Url : ADA313657

Report Date : JUL 1996

Pagination or Media Count : 24

Abstract : This paper deals with empirical Bayes selection procedures for selecting good exponential populations compared with a control. Based on the accumulated historical data, an empirical Bayes selection procedure delta(*) is constructed by mimicking the behavior of a Bayes selection procedure. The empirical Bayes selection procedure delta(*) is proved to be asympototically optimal. The analysis shows that the rate of convergence of delta(*) is influenced by the tail probabilities of the underlying distributions. It is shown that under certain regularity conditions on the moments of the prior distribution, the empirical Bayes selection procedure delta(*) is asymptotically optimal of order O(n(-lambda/2)) for some 0<lambda<2. A lower bound with rate of convergence of order O(n(-1)) is also established for the regret Bayes risk of the empirical Bayes selection procedure delta(*). This result suggests that a rate of order O(n(-1)) might be the best possible rate of convergence for this empirical Bayes selection problem.

Descriptors :   *NONPARAMETRIC STATISTICS, *BAYES THEOREM, OPTIMIZATION, PROBABILITY DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, STATISTICAL DATA, PROBABILITY DENSITY FUNCTIONS, CONVERGENCE, EXPONENTIAL FUNCTIONS, ASYMPTOTIC NORMALITY, POPULATION(MATHEMATICS).

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE