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.
Mots-clés : latent structure analysis, mixed distributions, identifiability, moment problem
@article{PS_2014__18__207_0,
author = {Kovtun, Mikhail and Akushevich, Igor and Yashin, Anatoliy},
title = {On identifiability of mixtures of independent distribution laws},
journal = {ESAIM: Probability and Statistics},
pages = {207--232},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2011166},
mrnumber = {3230875},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2011166/}
}
TY - JOUR AU - Kovtun, Mikhail AU - Akushevich, Igor AU - Yashin, Anatoliy TI - On identifiability of mixtures of independent distribution laws JO - ESAIM: Probability and Statistics PY - 2014 SP - 207 EP - 232 VL - 18 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2011166/ DO - 10.1051/ps/2011166 LA - en ID - PS_2014__18__207_0 ER -
%0 Journal Article %A Kovtun, Mikhail %A Akushevich, Igor %A Yashin, Anatoliy %T On identifiability of mixtures of independent distribution laws %J ESAIM: Probability and Statistics %D 2014 %P 207-232 %V 18 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2011166/ %R 10.1051/ps/2011166 %G en %F PS_2014__18__207_0
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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