NSF-CBMS Regional Conference Series in Probability and Statistics

Chapter 5: Decomposable measures

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The main purpose of this chapter is to discuss the extent to which Theorem 4.3 can be generalized to arbitrary Radon measures (rather than probability measures) and to cases where G is not compact. Such generalizations can be used in the derivation of densities of maximal invariants as well as in other areas. The approach here is modelled after that described in Andersson (1982). Other possible approaches to this problem are described in Wijsman (1986) (the global cross section approach using some Lie group theory) and Farrell (1985) (a measure-theoretic cross section approach developed by Schwartz (1966), unpublished).

Chapter information

Morris L. Eaton, Group Invariance in Applications in Statistics (Haywood, CA: Institute of Mathematical Sciences; Alexandria VA: American Statistical Association, 1989), 68-80

First available in Project Euclid: 1 May 2016

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Easton, Morris L. Chapter 5: Decomposable measures. Group invariance in applications in statistics, 68--80, Institute of Mathematical Statistics and American Statistical Association, Haywood CA and Alexandria VA, 1989. https://projecteuclid.org/euclid.cbms/1462061035

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