The Annals of Statistics

Characterization of Type from Maximal Invariant Spectra

Christopher G. Small

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Abstract

The affine type of distributions on the real line are represented as sequences of distributions of maximal invariants on spheres. It is shown that such a representation characterizes the affine type. A consistency condition is introduced, and it is shown that any sequence of maximal invariant distributions satisfying the condition is generated by some affine type on $\mathbf{R}$.

Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 979-983.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346263

Digital Object Identifier
doi:10.1214/aos/1176346263

Mathematical Reviews number (MathSciNet)
MR707947

Zentralblatt MATH identifier
0519.62001

JSTOR
links.jstor.org

Subjects
Primary: 62A05
Secondary: 62E10: Characterization and structure theory

Keywords
Maximal invariant statistic affine group type weak convergence

Citation

Small, Christopher G. Characterization of Type from Maximal Invariant Spectra. Ann. Statist. 11 (1983), no. 3, 979--983. doi:10.1214/aos/1176346263. https://projecteuclid.org/euclid.aos/1176346263


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