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January, 1975 Rates of Convergence in Empirical Bayes Estimation Problems: Continuous Case
Pi-Erh Lin
Ann. Statist. 3(1): 155-164 (January, 1975). DOI: 10.1214/aos/1176343005


In this paper we construct sequences of estimators for a density function and its derivatives, which are not assumed to be uniformly bounded, using classes of kernel functions. Utilizing these estimators, a sequence of empirical Bayes estimators is proposed. It is found that this sequence is asymptotically optimal in the sense of Robbins (Ann. Math. Statist. 35 (1964) 1-20). The rates of convergence of the Bayes risks associated with the proposed empirical Bayes estimators are obtained. It is noted that the exact rate is $n^{-q}$ with $q \leqq \frac{1}{3}$. An example is given and an explicit kernel function is indicated.


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Pi-Erh Lin. "Rates of Convergence in Empirical Bayes Estimation Problems: Continuous Case." Ann. Statist. 3 (1) 155 - 164, January, 1975.


Published: January, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0318.62027
MathSciNet: MR436405
Digital Object Identifier: 10.1214/aos/1176343005

Primary: 62F15
Secondary: 62F10

Keywords: Asymptotically optimal , empirical Bayes estimation , kernel function , rate of convergence , Squared error

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 1 • January, 1975
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