Simultaneous Inference, and Ranking Selection Procedure: Bayes and Empirical Bayes Approach

Abstract

Abstract : The research on simultaneous inference and ranking and selection procedures is important and relevant in comparing several populations (products, alternatives) in terms of their intrinsic quality or worth. This report embodies the research accomplishments in this broad area. The main contributions deal with newly developed ranking, selection and testing procedures based on Bayes and empirical Bayes approach. During the period April 1995 to September 2000, twenty-five research papers were completed by the PI and collaborators. Of these fifteen have been published and or accepted for publication in refereed journals and refereed conference proceedings volumes. The problems studied deal with a wide range of statistical models such as normal, Bernoulli, Poisson, and logistic distributions. In other papers, the statistical models are quite general in that the distributions are not specified but may belong to a broad family such as the positive or the general exponential family of distributions. One may want to know how good the empirical Bayes procedures are. This question is answered in terms of the convergence rate of the regret risk associated with empirical Bayes procedures. In general, it is found that the rate is optimal or very close to the optimal, where the optimal rate is the best achievable rate under certain conditions.