Empirical Bayes Testing for the Mean Lifetime of Exponential Distributions: Unequal Sample Sizes Case

摘要

This paper deals with an empirical Bayes testing problem for the mean lifetimes of exponential distributions with unequal sample sizes. We study a method to construct empirical Bayes tests {δ_(n+1,n)~*}_(n=1)~∞ for the sequence of the testing problems. The asymptotic optimality of {δ_(n+1,n)~*}_(n=1)~ ∞ is studied. It is shown that the sequence of empirical Bayes tests {δ_(n+1,n)~*}_(n=1)~ ∞ is asymptotically optimal, and its associated sequence of regrets converges to zero at a rate (ln n)~(4M-1), where M is an upper bound of sample sizes.