On empirical Bayes two-tail tests for double exponential distributions

Abstract

This paper deals with the problem of testing the hypotheses H 0 : |θ − θ 0 | ≤ c against H 1 : |θ − θ 0 | > c for the location parameter θ of a double exponential distribution with the probability density f (x|θ) = exp(−|x − θ |)/2 by using the empirical Bayes approach. We construct an empirical Bayes test δ * 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 δ * 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.