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

Hiroyuki Kasahara and Katsumi Shimotsu

Global COE Hi-Stat Discussion Paper Series from Institute of Economic Research, Hitotsubashi University

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.

Keywords: finite mixture; latent class analysis; nonnegative rank; rank estimation (search for similar items in EconPapers)
Date: 2012-10
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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:hst:ghsdps:gd12-247

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