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 {δ* nl + 1,n }∞ n = 1 for the sequence of the testing problems. The asymptotic optimality of {δ* nl + 1,n }∞ n = 1 is studied. It is shown that the sequence of empirical Bayes tests {δ* nl + 1,n }∞ n = 1 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.