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April 2000 On an empirical Bayes test for a normal mean
TaChen Liang
Ann. Statist. 28(2): 648-655 (April 2000). DOI: 10.1214/aos/1016218234


We exhibit an empirical Bayes test $\delta_n^*$ for the normal mean testing problem using a linear error loss. Under the condition that the critical point of a Bayes test is within some known compact interval, $\delta_n^*$ is shown to be asymptotically optimal and its associated regret Bayes risk converges to zero at a rate $O(n^{-1}(\ln n)^{1.5})$, where $n$ is the number of past experiences available when the current component decision problem is considered. Under the same condition this rate is faster than the optimal rate of convergence claimed by Karunamuni.


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TaChen Liang. "On an empirical Bayes test for a normal mean." Ann. Statist. 28 (2) 648 - 655, April 2000.


Published: April 2000
First available in Project Euclid: 15 March 2002

zbMATH: 1105.62301
MathSciNet: MR1790013
Digital Object Identifier: 10.1214/aos/1016218234

Primary: 62C12

Keywords: Asymptotically optimal , Empirical Bayes , rate of convergence

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 2 • April 2000
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