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May, 1980 Improving on Inadmissible Estimators in Continuous Exponential Families with Applications to Simultaneous Estimation of Gamma Scale Parameters
James Berger
Ann. Statist. 8(3): 545-571 (May, 1980). DOI: 10.1214/aos/1176345008

Abstract

A general technique is developed for improving upon inadmissible estimators of natural parameters (or integral powers thereof) from continuous exponential families. The technique is to reduce the problem to the study of a differential inequality. Typical differential inequalities are presented and solved. Explicit results are given for the simultaneous estimation of gamma scale parameters (and their inverses) for a variety of natural loss functions. Surprising behavior is observed for many of the estimators improving upon "standard" estimators. For squared error loss (and any continuous exponential family) it is shown explicitly how to establish inadmissibility of an estimator and construct improved estimators.

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James Berger. "Improving on Inadmissible Estimators in Continuous Exponential Families with Applications to Simultaneous Estimation of Gamma Scale Parameters." Ann. Statist. 8 (3) 545 - 571, May, 1980. https://doi.org/10.1214/aos/1176345008

Information

Published: May, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0447.62008
MathSciNet: MR568720
Digital Object Identifier: 10.1214/aos/1176345008

Subjects:
Primary: 62C15
Secondary: 62F10, 62H99

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 3 • May, 1980
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