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

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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
Keywords: latent structure analysis, mixed distributions, identifiability, moment problem 
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     title = {On identifiability of mixtures of independent distribution laws},
     journal = {ESAIM: Probability and Statistics},
     pages = {207--232},
     publisher = {EDP-Sciences},
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     year = {2014},
     doi = {10.1051/ps/2011166},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2011166/}
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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

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