Translator Disclaimer
December, 1988 Estimation of the Mixing Distribution for a Normal Mean with Applications to the Compound Decision Problem
David Edelman
Ann. Statist. 16(4): 1609-1622 (December, 1988). DOI: 10.1214/aos/1176351056

Abstract

A procedure for estimating the mixing distribution for a normal mean is presented. The estimator is shown to be consistent regardless of the mixing distribution, and it is suggested that the estimation techniques may be applied in a similar manner to estimate mixing distributions for a wide class of location parameter families. Implied marginal density and derivative estimates for the normal case are shown to be consistent, converging at near-optimal rates. In addition, empirical Bayes rules for the quadratic loss mean estimation problem which are derived from the estimated mixing distributions are shown to be asymptotically optimal in average compound risk and Bayes risk (if it is defined), provided the means are assumed to lie within a fixed range. A brief discussion of computational issues related to this estimation procedure is also included, along with some small-sample simulation results for the compound decision problem.

Citation

Download Citation

David Edelman. "Estimation of the Mixing Distribution for a Normal Mean with Applications to the Compound Decision Problem." Ann. Statist. 16 (4) 1609 - 1622, December, 1988. https://doi.org/10.1214/aos/1176351056

Information

Published: December, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0653.62008
MathSciNet: MR964941
Digital Object Identifier: 10.1214/aos/1176351056

Subjects:
Primary: 62C12
Secondary: 62C25

Rights: Copyright © 1988 Institute of Mathematical Statistics

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.16 • No. 4 • December, 1988
Back to Top