Title

Extended linear empirical Bayes estimation

Authors

M Pensky
P Ni

Comments

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Keywords

empirical Bayes; linear approximation; MODELS; Statistics & Probability

Abstract

In this paper, the linear empirical Bayes estimation method, which is based on approximation of the Bayes estimator by a linear function, is generalized to an extended linear empirical Bayes estimation technique which represents the Bayes estimator by a series of algebraic polynomials. The extended linear empirical Bayes estimators are elaborated in the case of a location or a scale parameter. The theory is illustrated by examples of its application to the normal distribution with a location parameter and the gamma distribution with a scale parameter. The linear and the extended linear empirical Bayes estimators are constructed in these two cases and, then, studied numerically via Monte Carlo simulations. The simulations show that the extended linear empirical Bayes estimators have better convergence rates than the traditional linear empirical Bayes estimators.

Publication Title

Communications in Statistics-Theory and Methods

Volume

29

Issue/Number

3

Publication Date

1-1-2000

Document Type

Article

Language

English

First Page

579

Last Page

592

WOS Identifier

WOS:000085700300007

ISSN

0361-0926

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