Proper action in steps, with application to density ratios of maximal invariants
type: Item
instance of: scholarly article
title: Proper action in steps, with application to density ratios of maximal invariants
zbMATH Open document ID: 0567.62003
author: Robert A. Wijsman
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: Let G be a locally compact group acting continuously on the left of a locally compact space \({\mathcal X}\). It is assumed that \(G=HK\) where H and K are closed subgroups. It is shown that if K acts properly on \({\mathcal X}\) and H acts properly on \({\mathcal X}/K\), then G acts properly on \({\mathcal X}\). 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.
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 57S99
zbMATH DE Number: 3905622
zbMATH Keywords: transformation group
zbMATH Keywords: orbit space
zbMATH Keywords: Cartan space
zbMATH Keywords: quotient measure
zbMATH Keywords: affine action
zbMATH Keywords: MANOVA
zbMATH Keywords: action on covariance matrices
zbMATH Keywords: canonical correlations
zbMATH Keywords: general MANOVA
zbMATH Keywords: locally compact group
zbMATH Keywords: locally compact space
zbMATH Keywords: composite actions
zbMATH Keywords: Proper action
zbMATH Keywords: density ratio of a maximal invariant
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346600
OpenAlex ID: W2037295216
DOI: 10.1214/AOS/1176346600
description: scientific article; zbMATH DE number 3905622