## The Annals of Statistics

### Minimal Sufficient Statistics for Families of Product Measures

D. Landers

#### 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

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