Empirical Bayes Testing for Double Exponential Distributions

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

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2007-06, Vol.36 (8), p.1543-1553
Main Author: Liang, Tachen
Format: Article
Language:English
Subjects:
Asymptotic optimality
Decision theory
Exact sciences and technology
General topics
Mathematics
Nonparametric inference
Parametric inference
Primary 62C12
Probability and statistics
Rate of convergence
Regret
Sciences and techniques of general use
Secondary 62C20
Statistics
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Summary:This article deals with the problem of testing the hypotheses H 0  : θ ≤ θ 0 against H 1  : θ > θ 0 for the location parameter θ of a double exponential distribution with probability density f(x | θ) = exp (−|x − θ|)/2 using the empirical Bayes approach. We construct an empirical Bayes test and study its associated asymptotic optimality. Three classes of prior distributions are considered. For priors in each class, the associated rates of convergence of 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.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610920601125987