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Monotone empirical Bayes tests for a discrete normal distribution

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  • Liang, TaChen

Abstract

We study the two-action problem in a discrete normal distribution via the empirical Bayes approach. An empirical Bayes test [delta]n* is constructed based on an estimator an* of the critical point aG of the Bayes test. The empirical Bayes test [delta]n* possesses the monotonicity and the asymptotic optimality, and its regret converges to zero at an exponential-type rate of order O(exp(-n[tau]G)), where [tau]G is a positive number, depending on the unknown prior distribution G.

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  • Liang, TaChen, 1999. "Monotone empirical Bayes tests for a discrete normal distribution," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 241-249, September.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:3:p:241-249
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    1. Balakrishnan, N. & Ma, Yimin, 1996. "Empirical Bayes rules for selecting the most and least probable multivariate hypergeometric event," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 181-188, April.
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    Cited by:

    1. R.J. Karunamuni & T. Liang & J. Wu, 2008. "Robust empirical Bayes tests for discrete distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(2), pages 101-113.
    2. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.

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