A mixture model for dimension reduction

Jean-Luc Dortet-Bernadet (1) , Laurent Gardes (1)

1 IRMA - Institut de Recherche Mathématique Avancée

The existence of a Dimension Reduction (DR) subspace is a common assumption in regression analysis when dealing with high-dimensional predictors. The estimation of such a DR subspace has received considerable attention in the past few years, the most popular method being undoubtedly the Sliced Inverse Regression suggested by Li. Nevertheless, this method is limited to univariate response variables and is known to fail in presence of regression symmetric relationships. To overcome these limitations, we propose in this paper a new estimation procedure of the DR subspace assuming that the joint distribution of the predictor and the response variables is a finite mixture of distributions. The new method is compared through a simulation study to some classical methods.

Mots clés: Dimension reduction; Maximum likelihood estimates; Mixture of distributions; Sliced Inverse Regression

Domaines: Statistiques [math.ST]

Jean-Luc Dortet-Bernadet, Laurent Gardes. A mixture model for dimension reduction. 2015. ⟨hal-01077146v2⟩