Nonparametric Identification and Estimation of the Number of Components in Multivariate Mixtures

Hiroyuki Kasahara and Katsumi Shimotsu
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Katsumi Shimotsu: Faculty of Economics, University of Tokyo

No CIRJE-F-866, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This 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.

Pages: 31 pages
Date: 2012-10
New Economics Papers: this item is included in nep-ecm
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Related works:
Journal Article: Non-parametric identification and estimation of the number of components in multivariate mixtures (2014)
Working Paper: Nonparametric Identification and Estimation of the Number of Components in Multivariate Mixtures (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2012cf866

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