## The Annals of Statistics

### Sufficient Statistics and Exponential Families

Christian Hipp

#### Abstract

Using a locally Lipschitz function $T$ of $n > 1$ variables one can reduce data consisting of a sample of size $n$ to one real number. If we are given a family of probability measures on the real line which are equivalent to Lebesgue measure then $T$ yields a sufficient data reduction only if the given family is exponential. This result is compared with the results of Brown (1964) and Denny (1970).

#### Article information

Source
Ann. Statist., Volume 2, Number 6 (1974), 1283-1292.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176342879

Digital Object Identifier
doi:10.1214/aos/1176342879

Mathematical Reviews number (MathSciNet)
MR378159

Zentralblatt MATH identifier
0294.62003

JSTOR