Section: New Results

A new sliced inverse regression method for multivariate response

Participants : Jérôme Saracco, Raphaël Coudret.

This work is in collaboration with Stéphane Girard (Inria Grenoble Alpes).

We consider a semiparametric regression model of a $q$-dimensional multivariate response $y$ on a $p$-dimensional covariate $x$. In this paper, a new approach is proposed based on sliced inverse regression for estimating the effective dimension reduction (EDR) space without requiring a prespecified parametric model. The convergence at rate $\sqrt{n}$ of the estimated EDR space is shown. We discuss the choice of the dimension of the EDR space. The numerical performance of the proposed multivariate SIR method is illustrated on a simulation study. Moreover, we provide a way to cluster components of $y$ related to the same EDR space. One can thus apply properly multivariate SIR on each cluster instead of blindly applying multivariate SIR on all components of $y$. An application to hyperspectral data is provided.

This work is currently under revision, see [48] .