Empirical bayes testing for the mean lifetime of exponential distributions: Unequal sample sizes case

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 {delta*(n+ 1,n)}(n=1)(infinity) for the sequence of the testing problems. The asymptotic optimality of {delta*(n+1,n)}(n=1)(infinity) is studied. It is shown that the sequence of empirical Bayes tests {delta*(n+1,n)}(n=1)(infinity) is asymptotically optimal, and its associated sequence of regrets converges to zero at a rate (ln n)(4M-1)/n, where M is an upper bound of sample sizes.