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March, 1975 Note on the Paper "Transformation Groups and Sufficient Statistics" by J. Pfanzagl
C. Hipp
Ann. Statist. 3(2): 478-482 (March, 1975). DOI: 10.1214/aos/1176343075

Abstract

Pfanzagl (1972) has shown that under suitable regularity conditions a family of probability measures which is generated by a transformation group and which for some sample size greater than one admits a sufficient statistic which is continuous, real-valued, and equivariant, is equivalent to the location parameter family of normal distributions or to a scale parameter family of Gamma distributions. This was proved under the assumption that the transformation group is Abelian. In this not commutativity of the group is replaced by local compactness.

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C. Hipp. "Note on the Paper "Transformation Groups and Sufficient Statistics" by J. Pfanzagl." Ann. Statist. 3 (2) 478 - 482, March, 1975. https://doi.org/10.1214/aos/1176343075

Information

Published: March, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0303.62007
MathSciNet: MR391311
Digital Object Identifier: 10.1214/aos/1176343075

Subjects:
Primary: 62B99
Secondary: 62E10

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • March, 1975
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