Empirical Bayes Testing for Uniform Distributions: Non Identical Components Case

Abstract

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 for the sequence of component testing problem. The asymptotic optimality of is studied. It has been shown that 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 α depending on conditions pertaining to the unknown prior distribution.

Keywords:

• Asymptotically optimal
• Non identical components
• Rate of convergence
• Regret

Mathematics Subject Classification:

• 62C12
• 62F15

Acknowledgments

The author would like to thank two referees for the careful review and valuable suggestions which lead to the improvement of the presentation of the article. This research was supported by NSC 97-2118-M-130-001 of the National Science Council of ROC.