On identifiability of mixtures of independent distribution laws
ESAIM: Probability and Statistics, Tome 18 (2014), pp. 207-232.

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.

DOI : 10.1051/ps/2011166
Classification : 60E99
Mots clés : latent structure analysis, mixed distributions, identifiability, moment problem
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Kovtun, Mikhail; Akushevich, Igor; Yashin, Anatoliy. On identifiability of mixtures of independent distribution laws. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 207-232. doi : 10.1051/ps/2011166. http://www.numdam.org/articles/10.1051/ps/2011166/

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