The Annals of Statistics

Sufficient Statistics and Exponential Families

Christian Hipp

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62B05: Sufficient statistics and fields
Secondary: 62E10: Characterization and structure theory 39A40

Keywords
Sufficient statistic characterization of exponential families

Citation

Hipp, Christian. Sufficient Statistics and Exponential Families. Ann. Statist. 2 (1974), no. 6, 1283--1292. doi:10.1214/aos/1176342879. https://projecteuclid.org/euclid.aos/1176342879


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