[hal-01077146] A mixture model for dimension reduction

In order to describe the relationship between a p-dimensional explanatory variable X and a response Y of dimension q when p is large the existence of a Dimension Reduction DR subspace is often assumed Estimation of such a DR subspace has received considerable attention in the past few years The most popular method is undoubtedly the Sliced Inverse Regression proposed by Li Nevertheless it is well known that it fails in presence of regression symmetric rela-tionships To overcome this limitation we propose in this paper a new estimation procedure of the DR subspace assuming that the random vector X Y follows a mixture of distributions The new method is compared through a simulation study to the classical methods SIR and SAVE



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