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On optimal convergence rate of empirical Bayes tests

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  • Liang, T.C.Ta Chen

Abstract

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.

Suggested Citation

  • Liang, T.C.Ta Chen, 2004. "On optimal convergence rate of empirical Bayes tests," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 189-198, June.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:2:p:189-198
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