Nonparametric Identification and Estimation of the Number of Components in Multivariate Mixtures
AbstractThis article analyzes the identifiability of the number of components in k-variate, M-component finite mixture models in which each component distribution has independent marginals, including models in latent class analysis. Without making parametric assumptions on the component distributions, we investigate how one can identify the number of components from the distribution function of the observed data. When k>= 2, a lower bound on the number of components (M) is nonparametrically identifiable from the rank of a matrix constructed from the distribution function of the observed variables. Building on this identification condition, we develop a procedure to consistently estimate a lower bound on the number of components.
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Bibliographic InfoPaper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd12-247.
Date of creation: Oct 2012
Date of revision:
finite mixture; latent class analysis; nonnegative rank; rank estimation;
Other versions of this item:
- Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Nonparametric Identification and Estimation of the Number of Components in Multivariate Mixtures," CIRJE F-Series CIRJE-F-866, CIRJE, Faculty of Economics, University of Tokyo.
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