On empirical Bayes two-tail tests for double exponential distributions

Lee-Shen Chen

Journal of Nonparametric Statistics, 2009, vol. 21, issue 8, 1037-1049

Abstract: This paper deals with the problem of testing the hypotheses H0: |θ−θ0|≤c against H1: |θ−θ0|>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.

Date: 2009
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DOI: 10.1080/10485250902971724

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