Proper Action in Steps, with Application to Density Ratios of Maximal Invariants
Wijsman, Robert A.
Ann. Statist., Tome 13 (1985) no. 1, p. 395-402 / Harvested from Project Euclid
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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.
Publié le : 1985-03-14
Classification:  Transformation group,  orbit space,  proper action,  Cartan space,  maximal invariant,  density ratio,  quotient measure,  composite action,  affine action,  MANOVA,  action on covariance matrices,  canonical correlations,  gerneral MANOVA,  62H10,  57S99 
@article{1176346600,
     author = {Wijsman, Robert A.},
     title = {Proper Action in Steps, with Application to Density Ratios of Maximal Invariants},
     journal = {Ann. Statist.},
     volume = {13},
     number = {1},
     year = {1985},
     pages = { 395-402},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176346600}
}

Wijsman, Robert A. Proper Action in Steps, with Application to Density Ratios of Maximal Invariants. Ann. Statist., Tome 13 (1985) no. 1, pp.  395-402. http://gdmltest.u-ga.fr/item/1176346600/