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ON EMPIRICAL BAYES ESTIMATION IN THE LOCATION FAMILY 

Authors: R. J. Karunamuni a;  R. S. Singh b; ZHANG c
Affiliations:   a Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1.
b Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1.
c Department of Mathematical Sciences, University of Alaska, Fairbanks, Alaska, U.S.A. 99775.
DOI: 10.1080/10485250213113
Publication Frequency: 8 issues per year
Published in: journal Journal of Nonparametric Statistics, Volume 14, Issue 4 2002 , pages 435 - 448
Number of References: 30
Formats available: PDF (English)
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Abstract

This paper considers empirical Bayes (EB) squared error loss estimation (SELE) in the location family. That is, the component problem is the SELE of <$>\theta<$> based on an observation Y having conditional (on <$>\theta<$>) density of the form <$>f_lcub0rcub(y - \theta)<$> for some known density function <$>f_lcub0rcub<$>. An EB estimator is constructed based on kernel type estimator of the unknown prior density using deconvolution techniques. It is shown that the proposed EB estimator is asymptotically optimal. Uniform rates of convergence of the regret are also exhibited. This paper presents a generalization to the existing results on the same problem considered for the normal <$>(\theta, 1)<$> uniform <$>(\theta, \theta + 1)<$> and translated exponential <$>(\theta)<$> distributions.
Keywords: Bayes; Empirical Bayes; Squared Error Loss Estimation; Kernel Density Estimates; Asymptotically Optimal; Location Family
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