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Identifiability of mixtures

Part of: Distribution theory

Published online by Cambridge University Press:  09 April 2009

G. M. Tallis  and
P. Chesson
G. M. Tallis
Affiliation:
Department of Statistics, University of Adelaide, Adelaide, S. A. 5001, Australia
P. Chesson
Affiliation:
Department of Statistics, University of Adelaide, Adelaide, S. A. 5001, Australia
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Abstract

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Let F(x, θ) be a family of distribution functions indexed by θ ∈ Ω. If G(θ) is a distribution function on Ω H(x) = ƒohm; F(x, θ) dG(θ) is a mixture with respect to G. If there is a unique G yielding H, the mixtures is said to be identifiable.This paper summarises some known results related to identifiability of special types of mixtures and then discusses the general problem of identifiability in terms of mappings. Some new results follow for mappings with special features.

Keywords

mixtureidentifiabilitykernellinear independencestrong indendencebounded inveseundounded inverse

MSC classification

Secondary: 62E10: Characterization and structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 3 , June 1982 , pp. 339 - 348
Copyright
Copyright © Australian Mathematical Society 1982

References

Barndoff-Nielsen, O. (1965), ‘Identifiability of mixtures of exponential families’, J. Math. Anal. Appl. 12, 115–121.CrossRefGoogle Scholar
Breiman, L. (1968), Probability (Addison-Wesley).Google Scholar
Maritz, J. S. (1970), Empirical Bayes methods (Methuen, London).Google Scholar
Patil, G. P. and Bildekar, S. (1966), ‘Identifiability of countable mixtures of discrete probability distributions using methods of infinite matrices’, Proc. Cambridge Philos. Soc. 62, 485–494.CrossRefGoogle Scholar
Parthasarathy, K. R. (1967), Probability measures on metric spaces (Academic Press, New York).CrossRefGoogle Scholar
Tallis, G. M., ‘The identifiability of mixtures of distributions’, J. Appl. Probability 6, 389–398.CrossRefGoogle Scholar
Teicher, H. (1963), ‘Identifiability of finite mixtures’, Ann. Math. Statist. 34, 1265–1269.CrossRefGoogle Scholar