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On identifiability of mixtures of independent distributionlaws∗∗∗∗∗∗

Published online by Cambridge University Press:  01 July 2014

Mikhail Kovtun ,
Igor Akushevich  and
Anatoliy Yashin
Mikhail Kovtun
Affiliation:
Duke University, Dept. of Biology, Benfey Lab Durham, 27708 NC, USA. mikhail.kovtun@duke.edu
Igor Akushevich
Affiliation:
Center for Population Health and Aging Durham, 27708 NC, USA; igor.akushevich@duke.edu; anatoly.yashin@duke.edu
Anatoliy Yashin
Affiliation:
Center for Population Health and Aging Durham, 27708 NC, USA; igor.akushevich@duke.edu; anatoly.yashin@duke.edu
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Abstract

We consider representations of a joint distribution law of a family of categorical randomvariables (i.e., a multivariate categorical variable) as a mixture ofindependent distribution laws (i.e. distribution laws according to whichrandom variables are mutually independent). For infinite families of random variables, wedescribe a class of mixtures with identifiable mixing measure. This class is interestingfrom a practical point of view as well, as its structure clarifies principles of selectinga “good” finite family of random variables to be used in applied research. For finitefamilies of random variables, the mixing measure is never identifiable; however, it alwayspossesses a number of identifiable invariants, which provide substantial informationregarding the distribution under consideration.

Keywords

Latent structure analysismixed distributionsidentifiabilitymoment problem
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 207 - 232
Copyright
© EDP Sciences, SMAI 2014

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References

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