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July, 1978 Solutions to Empirical Bayes Squared Error Loss Estimation Problems
Richard J. Fox
Ann. Statist. 6(4): 846-853 (July, 1978). DOI: 10.1214/aos/1176344258

Abstract

Asymptotically optimal empirical Bayes squared error loss estimation procedures are developed for three families of continuous distributions, uniform $(0, \theta), \theta > 0,$ uniform $\lbrack \theta, \theta + 1), \theta$ arbitrary, and a location parameter family of gamma distributions. The approach taken is to estimate the Bayes estimator directly. However, for the $\lbrack \theta, \theta + 1)$ case, it is shown that the indirect approach of applying the Bayes estimator, versus an almost sure weakly convergent estimator of the prior, also yields an asymptotically optimal procedure.

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Richard J. Fox. "Solutions to Empirical Bayes Squared Error Loss Estimation Problems." Ann. Statist. 6 (4) 846 - 853, July, 1978. https://doi.org/10.1214/aos/1176344258

Information

Published: July, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62003
MathSciNet: MR494607
Digital Object Identifier: 10.1214/aos/1176344258

Subjects:
Primary: 62C25
Secondary: 62A15 , 62C10 , 62F10 , 62F15

Keywords: asymptotically optimal empirical Bayes procedure , Bayes optimal risk , Empirical Bayes squared error loss estimation , posterior mean

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 4 • July, 1978
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