Section: New Results

A new sliced inverse regression method for multivariate response

Participants : Jérôme Saracco, Raphaël Coudret.

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 e ffective dimension reduction (EDR) space without requiring a prespeci ed parametric model. The convergence at rate square root of 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.

These results have been obtained in collaboration with Stéphane Girard (Inria Rhône Alpes).

The paper is under revision for possible publication in CSDA [63] .