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On empirical Bayes two-tail tests for double exponential distributions

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  • Lee-Shen Chen

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.

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  • Lee-Shen Chen, 2009. "On empirical Bayes two-tail tests for double exponential distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(8), pages 1037-1049.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:8:p:1037-1049
    DOI: 10.1080/10485250902971724
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    1. Huang, Wen-Tao & Huang, Hui-Hsin, 2006. "Empirical Bayes estimation of the guarantee lifetime in a two-parameter exponential distribution," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1821-1829, October.
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