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Models and estimation algorithms for nonparametric finite mixtures with conditionally independent multivariate component densities

Abstract : Recently several authors have proposed models and estimation algorithms for finite nonparametric multivariate mixtures, whose identifiability is typically not obvious. Among the considered models, the assumption of independent coordinates conditional on the subpopulation from which each observation is drawn is subject of an increasing attention, in view of the theoretical and practical developments it allows, particularly with multiplicity of variables coming into play in the modern statistical framework. In this work we first consider a more general model assuming independence, conditional on the component, of multivariate blocks of coordinates instead of univariate coordinates, allowing for any dependence structure within these blocks. Consequently, the density functions of these blocks are completely multivariate and nonparametric. We present identifiability arguments and introduce for estimation in this model two methodological algorithms whose computational procedures resemble a true EM algorithm but include an additional density estimation step: a fast algorithm showing empirical efficiency without theoretical justification, and a smoothed algorithm possessing a monotony property as any EM algorithm does, but more computationally demanding. We also discuss computationally efficient methods for estimation and derive some strategies. Next, we consider a multivariate extension of the mixture models used in the framework of multiple hypothesis testings, allowing for a new multivariate version of the False Discovery Rate control. We propose a constrained version of our previous algorithm, specifically designed for this model. The behavior of the EM-type algorithms we propose is studied numerically through several Monte Carlo experiments and high dimensional real data, and compared with existing methods in the literature. Finally, the codes of our new algorithms are progressively implemented as new functions in the publicly-available package mixtools for the R statistical software.
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https://tel.archives-ouvertes.fr/tel-01713125
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Vy-Thuy-Lynh Hoang. Models and estimation algorithms for nonparametric finite mixtures with conditionally independent multivariate component densities. General Mathematics [math.GM]. Université d'Orléans, 2017. English. ⟨NNT : 2017ORLE2012⟩. ⟨tel-01713125⟩

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