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.
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.