On empirical Bayes two-tail tests for double exponential distributions

This paper deals with the problem of testing the hypotheses H(0): vertical bar theta - theta(0)vertical bar <= c against H(1): vertical bar theta - theta(0)vertical bar > c for the location parameter theta of a double exponential distribution with the probability density f (x vertical bar theta) = exp(-| x - theta|)/2 by using the empirical Bayes approach. We construct an empirical Bayes test delta(n)* and study its associated asymptotic optimality. Three classes of prior distributions are considered. For priors in each class, the associated rates of convergence of delta(n)* are established. These rates are O(n(-2m/(2m+ 3))), O((ln n)(3/s)/n), and O(n(-1)), respectively, where m > 1 and s >= 1 are determined according to some conditions.