## The Annals of Statistics

- Ann. Statist.
- Volume 2, Number 6 (1974), 1335-1339.

### Minimal Sufficient Statistics for Families of Product Measures

#### Abstract

It is shown in this paper that the product family of countably many families of perfect probability measures defined on countably generated $\sigma$-fields admits a minimal sufficient statistic if and only if each component family admits a minimal sufficient statistic. Moreover, the minimal sufficient statistic of the product family is the "product" of the minimal sufficient statistics for the component families. Examples show that the assumptions on the component families cannot be omitted.

#### Article information

**Source**

Ann. Statist., Volume 2, Number 6 (1974), 1335-1339.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176342887

**Digital Object Identifier**

doi:10.1214/aos/1176342887

**Mathematical Reviews number (MathSciNet)**

MR378160

**Zentralblatt MATH identifier**

0295.62005

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62B05: Sufficient statistics and fields

**Keywords**

Minimal sufficient statistic product measures

#### Citation

Landers, D. Minimal Sufficient Statistics for Families of Product Measures. Ann. Statist. 2 (1974), no. 6, 1335--1339. doi:10.1214/aos/1176342887. https://projecteuclid.org/euclid.aos/1176342887