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March, 1985 Proper Action in Steps, with Application to Density Ratios of Maximal Invariants
Robert A. Wijsman
Ann. Statist. 13(1): 395-402 (March, 1985). DOI: 10.1214/aos/1176346600

Abstract

Let $G$ be a locally compact group acting continuously on the left of a locally compact space $\mathscr{X}$. It is assumed that $G = HK$ where $H$ and $K$ are closed subgroups. It is shown that if $K$ acts properly on $\mathscr{X}$ and $H$ acts properly on $\mathscr{X}/K$, then $G$ acts properly on $\mathscr{X}$. Under a mild additional condition the converse is also true. Several examples are given to show how these results can help decide the properness of composite actions. Proper action can be used to justify the representation of the density ratio of a maximal invariant as a ratio of integrals over the group.

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Robert A. Wijsman. "Proper Action in Steps, with Application to Density Ratios of Maximal Invariants." Ann. Statist. 13 (1) 395 - 402, March, 1985. https://doi.org/10.1214/aos/1176346600

Information

Published: March, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0567.62003
MathSciNet: MR773175
Digital Object Identifier: 10.1214/aos/1176346600

Subjects:
Primary: 62H10
Secondary: 57S99

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 1 • March, 1985
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