Volume 18, 2014
|Page(s)||207 - 232|
|Published online||01 July 2014|
1 Duke University, Dept. of Biology, Benfey Lab Durham, 27708
2 Center for Population Health and Aging Durham, 27708 NC, USA
Revised: 26 March 2011
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.
Mathematics Subject Classification: 60E99
Key words: Latent structure analysis / mixed distributions / identifiability / moment problem
The work of the first author was supported by the Office of Vice Provost for Research, Duke University.
The work of the second author was supported by NIA grants R01AG030198, R01AG028259, and R01AG032319.
© EDP Sciences, SMAI 2014
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