Accession Number : ADA193341

Title :   Selecting the Best Binomial Population: Parametric 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 : ADA193341

Report Date : 01 Feb 1988

Pagination or Media Count : 21

Abstract : Consider k populations pi(1),...,pi(k), where an observation from population pi(i) has a binomial distribution with parameters N and p sub i (unknown). Let p/k/ = max over 1 or = j or = k p sub j. A population pi(i) with p sub i = p/k/ is called a best population. We are interested in selecting the best population. Let p = (p sub 1,..., p sub k) and let a denote the index of the selected population. Under the loss function L(p, a) = p /k/ - p sub a, this statistical selection problem is studied via a parametric empirical Bayes approach. It is assumed that the binomial parameters p sub i, i = 1,...,k, follow some conjugate beta prior distributions with unknown hyperparameters. Under the binomial-beta statistical framework, an empirical Bayes selection rule is proposed. It is shown that the Bayes risk of the proposed empirical Bayes selection rule converges to the corresponding minimum Bayes risk with rates of convergence at least of order O(exp(-cn)) for some positive constant c, where n is the number of accumulated past experience (observations) at hand. Keywords: Asymptotically optimal; Bayes rules; Empirical Bayes rules; Best population; Binomial beta model; Rate of convergence.

Descriptors :   *BINOMIALS, *STATISTICAL DISTRIBUTIONS, *POPULATION(MATHEMATICS), APPROACH, BAYES THEOREM, CONVERGENCE, PARAMETRIC ANALYSIS, POPULATION, RATES, RISK, SELECTION, MATHEMATICAL MODELS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE