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November, 1978 Universal Bayes Estimators
A. L. Rukhin
Ann. Statist. 6(6): 1345-1351 (November, 1978). DOI: 10.1214/aos/1176344379

Abstract

Let $x_1, \cdots, x_n$ be i.i.d. random variables with a distribution depending on the real parameter. Under what conditions is a generalized Bayes estimator independent of the choice of the even loss function? The known answer to this question is that this independence holds if the posterior density is symmetric and unimodal. The description of distributions and corresponding generalized prior densities on the real line, for which the posterior density is symmetric and unimodal, is presented. These families form an important subclass of all exponential laws with two-dimensional sufficient statistics.

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A. L. Rukhin. "Universal Bayes Estimators." Ann. Statist. 6 (6) 1345 - 1351, November, 1978. https://doi.org/10.1214/aos/1176344379

Information

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

zbMATH: 0392.62023
MathSciNet: MR523768
Digital Object Identifier: 10.1214/aos/1176344379

Subjects:
Primary: 62F10
Secondary: 62C10

Keywords: generalized Bayes estimators , loss function , unimodal and symmetrical posterior density , universal estimators

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 6 • November, 1978
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