A new sliced inverse regression method for multivariate response

Raphaël Coudret (1, 2, 3) , Stéphane Girard (4) , Jerome Saracco (1, 2, 5)

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
5 ENSC - Ecole Nationale Supérieure de Cognitique

A semiparametric regression model of a q-dimensional multivariate response y on a p-dimensional covariate x is considered. A new approach is proposed based on sliced inverse regression (SIR) for estimating the effective dimension reduction (EDR) space without requiring a prespecified parametric model. The convergence at rate square root of n of the estimated EDR space is shown. The choice of the dimension of the EDR space is discussed. Moreover, a way to cluster components of y related to the same EDR space is provided. Thus, the proposed multivariate SIR method can be used properly on each cluster instead of blindly applying it on all components of y. The numerical performances of multivariate SIR are illustrated on a simulation study. Applications to a remote sensing dataset and to the Minneapolis elementary schools data are also provided. Although the proposed methodology relies on SIR, it opens the door for new regression approaches with a multivariate response.

Mots clés: Semiparametric regression model; Dimension reduction; Sliced inverse regression; Multivariate response

Domaines: Méthodologie [stat.ME]

Raphaël Coudret, Stéphane Girard, Jerome Saracco. A new sliced inverse regression method for multivariate response. Computational Statistics and Data Analysis, 2014, 77, pp.285-299. ⟨10.1016/j.csda.2014.03.006⟩. ⟨hal-00714981v3⟩