The Annals of Statistics

Improving on Inadmissible Estimators in Continuous Exponential Families with Applications to Simultaneous Estimation of Gamma Scale Parameters

James Berger

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 8, Number 3 (1980), 545-571.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345008

Digital Object Identifier
doi:10.1214/aos/1176345008

Mathematical Reviews number (MathSciNet)
MR568720

Zentralblatt MATH identifier
0447.62008

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62F10: Point estimation 62H99: None of the above, but in this section

Keywords
Inadmissible estimators exponential families gamma scale parameters differential inequalities simultaneous estimation

Citation

Berger, James. Improving on Inadmissible Estimators in Continuous Exponential Families with Applications to Simultaneous Estimation of Gamma Scale Parameters. Ann. Statist. 8 (1980), no. 3, 545--571. doi:10.1214/aos/1176345008. https://projecteuclid.org/euclid.aos/1176345008


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