A new sliced inverse regression method for multivariate response regression

Raphaël Coudret (1, 2, 3) , Stéphane Girard (4) , Jerome Saracco (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability
3 EPOC - Environnements et Paléoenvironnements OCéaniques
4 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems

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.

Domaines: Méthodologie [stat.ME]

Raphaël Coudret, Stéphane Girard, Jerome Saracco. A new sliced inverse regression method for multivariate response regression. 2012. ⟨hal-00714981v1⟩