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December, 1970 Global Cross Sections and the Densities of Maximal Invariants
Uwe Koehn
Ann. Math. Statist. 41(6): 2045-2056 (December, 1970). DOI: 10.1214/aoms/1177696704


This paper generalizes some results of Wijsman concerning the calculation of the density of a maximal invariant. The idea of the technique is to represent the sample space as a product space, one factor $Z$ being a global cross section, i.e., essentially a set that intersects each orbit in a unique point, and the other factor being a coset space of the invariance group. Integration over the invariance group then gives the distribution of the identity function on $Z$ which is a maximal invariant. Part I of the paper gives sufficient conditions for the technique to be applicable, while Part II exhibits the technique along with an example. Part II is on a more elementary level than Part I and may be understood without a reading of Part I.


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Uwe Koehn. "Global Cross Sections and the Densities of Maximal Invariants." Ann. Math. Statist. 41 (6) 2045 - 2056, December, 1970.


Published: December, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0215.26404
MathSciNet: MR270478
Digital Object Identifier: 10.1214/aoms/1177696704

Rights: Copyright © 1970 Institute of Mathematical Statistics


Vol.41 • No. 6 • December, 1970
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