Empirical Bayes Testing for Uniform Distributions: Non Identical Components Case

摘要

This article deals with non identical components empirical Bayes testing for uniform distributions. First, we derive the Bayes rule. Then, by mimicking the behavior of the preceding Bayes rule, we construct a sequence of empirical Bayes tests {δ_(n+1, n)*} for the sequence of component testing problem. The asymptotic optimality of {δ_(n+1,n)*} is studied. It has been shown that {δ_(n+1,n)*} possesses the asymptotic optimality, and the associated sequence of regrets converge to zero at a rate O((n~(-2(r+α)/[2(r+α)+1), where n is the number of past data available when the present testing problem is considered, and r is a positive integer, 0 ≤ α ≤ 1, r and a depending on conditions pertaining to the unknown prior distribution.