On identifiability of mixtures of independent distribution laws∗∗∗∗∗∗. (1st July 2014)

• Record Type: Journal Article
• Authors: Kovtun, Mikhail; Akushevich, Igor; Yashin, Anatoliy
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 207
• Page End: 232
• Publication Date: 2014-07-01
• Subjects: Latent structure analysis, -- mixed distributions, -- identifiability, -- moment problem; Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2011166
• Languages: English
• ISSNs: 1292-8100

Abstract

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.