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November, 1974 Sufficient Statistics and Exponential Families
Christian Hipp
Ann. Statist. 2(6): 1283-1292 (November, 1974). DOI: 10.1214/aos/1176342879

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).

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Christian Hipp. "Sufficient Statistics and Exponential Families." Ann. Statist. 2 (6) 1283 - 1292, November, 1974. https://doi.org/10.1214/aos/1176342879

Information

Published: November, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0294.62003
MathSciNet: MR378159
Digital Object Identifier: 10.1214/aos/1176342879

Subjects:
Primary: 62B05
Secondary: 39A40, 62E10

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 6 • November, 1974
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