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Empirical Bayes testing for success probability of Bernoulli process with negative binomial sampling: nonidentical components case

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Abstract

We study an empirical Bayes testing problem for the success probability of Bernoulli process with negative binomial sampling under nonidentical components situation. An empirical Bayes test δ * n+1,n is constructed based on an estimator c n of the critical point c G of the Bayes test δ n+1,G . The empirical Bayes test δ * n+1,n possesses the asymptotic optimality, and its associated regret converges to zero at an exponential decay rate O(exp (−n α)) for some positive value α, depending on the unknown prior distribution G. This result extends the exponential type decay rate of convergence obtained in Liang (Ann. Stat. 16:1635–1642, 1988; Stat. Probab. Lett. 44:241–249, 1999) to the nonidentical components case.

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  1. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    TaChen Liang

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  1. TaChen Liang
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Correspondence to TaChen Liang.

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Liang, T. Empirical Bayes testing for success probability of Bernoulli process with negative binomial sampling: nonidentical components case. J. Appl. Math. Comput. 30, 427–437 (2009). https://doi.org/10.1007/s12190-008-0182-9

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  • DOI: https://doi.org/10.1007/s12190-008-0182-9

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