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2015 Semi-parametric estimation for conditional independence multivariate finite mixture models
Didier Chauveau, David R. Hunter, Michael Levine
Statist. Surv. 9: 1-31 (2015). DOI: 10.1214/15-SS108


The conditional independence assumption for nonparametric multivariate finite mixture models, a weaker form of the well-known conditional independence assumption for random effects models for longitudinal data, is the subject of an increasing number of theoretical and algorithmic developments in the statistical literature. After presenting a survey of this literature, including an in-depth discussion of the all-important identifiability results, this article describes and extends an algorithm for estimation of the parameters in these models. The algorithm works for any number of components in three or more dimensions. It possesses a descent property and can be easily adapted to situations where the data are grouped in blocks of conditionally independent variables. We discuss how to adapt this algorithm to various location-scale models that link component densities, and we even adapt it to a particular class of univariate mixture problems in which the components are assumed symmetric. We give a bandwidth selection procedure for our algorithm. Finally, we demonstrate the effectiveness of our algorithm using a simulation study and two psychometric datasets.


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Didier Chauveau. David R. Hunter. Michael Levine. "Semi-parametric estimation for conditional independence multivariate finite mixture models." Statist. Surv. 9 1 - 31, 2015.


Published: 2015
First available in Project Euclid: 6 February 2015

zbMATH: 1307.62090
MathSciNet: MR3310969
Digital Object Identifier: 10.1214/15-SS108

Primary: 62G05
Secondary: 62G07

Keywords: kernel density estimation , MM algorithms

Rights: Copyright © 2015 The author, under a Creative Commons Attribution License


Vol.9 • 2015
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