Empirical Bayes testing for double exponential distributions

This article deals with the problem of testing the hypotheses H-0 : theta <= theta(0) against H-1 : theta > theta(0) for the location parameter theta of a double exponential distribution with probability density f(x vertical bar theta) = exp(-vertical bar x - theta vertical bar)/2 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. The rates are: O(n(-(2m+1)/(2m+2))), O(n(-1)(ln n)1/s), and O(n(-1)), respectively, where m >= 1 and s > 0.