The Annals of Statistics

A Useful Empirical Bayes Identity

Noel Cressie

Full-text: Open access

Abstract

For any decision problem, one wishes to find that estimator which minimizes the expected loss. If the loss function is squared error, then the estimator is the mean of the Bayes posterior distribution. Unfortunately the prior distribution may be unknown, but in certain situations empirical Bayes methods can circumvent this problem by using past observations to estimate either the prior or the Bayes estimate directly. Empirical Bayes methods are particularly appealing when the Bayes estimate depends only on the marginal distribution of the observed variable, yielding what is known as a simple empirical Bayes estimate. The paper looks at the underlying circumstance of when a simple empirical Bayes estimator is available, and shows its occurrence not to be happenstance.

Article information

Source
Ann. Statist., Volume 10, Number 2 (1982), 625-629.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345804

Digital Object Identifier
doi:10.1214/aos/1176345804

Mathematical Reviews number (MathSciNet)
MR653538

Zentralblatt MATH identifier
0492.62030

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62P15: Applications to psychology

Keywords
Bayes estimator binomial model exponential families linear functionals power series distribution

Citation

Cressie, Noel. A Useful Empirical Bayes Identity. Ann. Statist. 10 (1982), no. 2, 625--629. doi:10.1214/aos/1176345804. https://projecteuclid.org/euclid.aos/1176345804


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