Selecting the Best Binomial Population: Parametric Empirical Bayes Approach.
PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS
Pagination or Media Count:
Consider k populations pi1,...,pik, where an observation from population pii has a binomial distribution with parameters N and p sub i unknown. Let pk max over 1 or j or k p sub j. A population pii with p sub i pk 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 Lp, 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 Oexp-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.
- Statistics and Probability