The Annals of Statistics

Note on the Paper "Transformation Groups and Sufficient Statistics" by J. Pfanzagl

C. Hipp

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 3, Number 2 (1975), 478-482.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343075

Digital Object Identifier
doi:10.1214/aos/1176343075

Mathematical Reviews number (MathSciNet)
MR391311

Zentralblatt MATH identifier
0303.62007

JSTOR
links.jstor.org

Subjects
Primary: 62B99: None of the above, but in this section
Secondary: 62E10: Characterization and structure theory

Keywords
Sufficiency normal distribution Gamma distribution

Citation

Hipp, C. Note on the Paper "Transformation Groups and Sufficient Statistics" by J. Pfanzagl. Ann. Statist. 3 (1975), no. 2, 478--482. doi:10.1214/aos/1176343075. https://projecteuclid.org/euclid.aos/1176343075


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