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On identifiability of mixtures of independent distribution laws∗∗∗∗∗∗

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 random variables (i.e., a multivariate categorical variable) as a mixture of independent distribution laws (i.e. distribution laws according to which random variables are mutually independent). For infinite families of random variables, we describe a class of mixtures with identifiable mixing measure. This class is interesting from a practical point of view as well, as its structure clarifies principles of selecting a “good” finite family of random variables to be used in applied research. For finite families of random variables, the mixing measure is never identifiable; however, it always possesses a number of identifiable invariants, which provide substantial information regarding 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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