ON IDENTIFIABILITY OF MIXTURES OF INDEPENDENT DISTRIBUTION LAWS(, .)

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2014-01

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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.

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10.1051/ps/2011166

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Kovtun, Mikhail, Igor Akushevich and Anatoliy Yashin (2014). ON IDENTIFIABILITY OF MIXTURES OF INDEPENDENT DISTRIBUTION LAWS(, .). ESAIM Probab Stat, 18. pp. 207–232. 10.1051/ps/2011166 Retrieved from https://hdl.handle.net/10161/14829.

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Scholars@Duke

Kovtun

Mikhail Kovtun

Biostatistician III

Igor Akushevich

Research Professor in the Social Science Research Institute
Yashin

Anatoli I. Yashin

Research Professor in the Social Science Research Institute

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