## The Annals of Statistics

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

### A Useful Empirical Bayes Identity

#### 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