## The Annals of Mathematical Statistics

### Minimal Sufficient $|sigma$-Fields and Minimal Sufficient Statistics. Two Counterexamples

#### Abstract

In this paper there are solved two problems raised by Bahadur (1954) which concern the relation between the existence of a minimal sufficient $\sigma$-field and the existence of a minimal sufficient statistic. Two examples show that the existence of a minimal sufficient $\sigma$-field is neither necessary nor sufficient for the existence of a minimal sufficient statistic.

#### Article information

Source
Ann. Math. Statist., Volume 43, Number 6 (1972), 2045-2049.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177690882

Digital Object Identifier
doi:10.1214/aoms/1177690882

Mathematical Reviews number (MathSciNet)
MR353519

Zentralblatt MATH identifier
0256.62005

JSTOR
Landers, Dieter; Rogge, Lothar. Minimal Sufficient $|sigma$-Fields and Minimal Sufficient Statistics. Two Counterexamples. Ann. Math. Statist. 43 (1972), no. 6, 2045--2049. doi:10.1214/aoms/1177690882. https://projecteuclid.org/euclid.aoms/1177690882