On empirical bayes rules for selecting the best hypergeometric population

Abstract

In this paper, we consider k hypergeometric populations π_i = π(M_i,m_i,s_i), i=1,…,k, where M_i is the number of units in population π_i, m_i is the number of units selected from π_i, and s_i is the number of defective units in π_i . Let . A population π_i with is considered as a best population. We are interested in selecting the best population and the best population compared with a control. It is assumed that the unknown parameteres s_i i = 1,…,k, follow some binomial prior distribution with unknown hyperparameters. Under the hypergeometric-binomial model, two empirical Bayes selection rules are studied according to the different selection problems. It is shown that for each empirical Bayes selection rule, the corresponding Bayes risk tends to the minimum Bayes risk with a rate of convergence of order O(exp(-cn)) for some positive constant c, where the value of c varies depending on the rule and n is the number of accumulated past observations.

Keywords:

• Bayes rules
• Best population
• Empirical Bayes rules
• Hypergeometric-binomial model
• Rate of convergence

Additional information

Notes on contributors

N. Balakrishnan

Yimin Ma