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February 1996 Optimal rates of convergence of empirical Bayes tests for the continuous one-parameter exponential family
Rohana J. Karunamuni
Ann. Statist. 24(1): 212-231 (February 1996). DOI: 10.1214/aos/1033066207

Abstract

The empirical Bayes linear loss two-action problem in the continuous one-parameter exponential family is studied. Previous results on this problem construct empirical Bayes tests via kernel density estimates. They also obtain upper bounds for the unconditional regret at some prior distribution. In this paper, we discuss the general question of how difficult the above empirical Bayes problem is, and why empirical Bayes rules based on kernel density estimates are useful. Asymptotic minimax-type lower bounds are obtained for the unconditional regret, and empirical Bayes rules based on kernel density estimates are shown to possess a certain optimal asymptotic minimax property.

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Rohana J. Karunamuni. "Optimal rates of convergence of empirical Bayes tests for the continuous one-parameter exponential family." Ann. Statist. 24 (1) 212 - 231, February 1996. https://doi.org/10.1214/aos/1033066207

Information

Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0853.62011
MathSciNet: MR1389888
Digital Object Identifier: 10.1214/aos/1033066207

Subjects:
Primary: 62C12
Secondary: 62C20, 62F03

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 1 • February 1996
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