On optimal convergence rate of empirical Bayes tests
This paper deals with the optimal convergence rate of empirical Bayes tests. A sharp lower bound on the minimax regret of empirical Bayes tests is established. When the result is applied to the normal distribution model, a lower convergence rate n-1 is obtained. We also construct an empirical Bayes test [delta]n* whose corresponding regret achieves the rate n-1, provided that [psi]G, the characteristic function of the prior distribution G, is such that [psi]G(t)=0 for t[greater-or-equal, slanted]b-1 for some b>0. Therefore, for the empirical Bayes testing for a normal mean problem, the optimal convergence rate is n-1.
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Volume (Year): 68 (2004)
Issue (Month): 2 (June)
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