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

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  • Kasahara Hiroyuki
  • Shimotsu Katsumi

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.

Suggested Citation

  • Kasahara Hiroyuki & Shimotsu Katsumi, 2012. "Nonparametric Identification and Estimation of the Number of Components in Multivariate Mixtures," Global COE Hi-Stat Discussion Paper Series gd12-247, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:ghsdps:gd12-247
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    References listed on IDEAS

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