Résumé 249 :

Semi-parametric single index models (SIM) are now widely used by the statisticians. For mean regressions, the SIM assumption means that the conditional expectation of the response given the vector of covariates is the same as the conditional expectation of the response given a linear combination of the covariates. Recently, this idea was extended to quantile regression. When modeling the conditional distribution of an observed variable given the covariates, under the SIM assumption the response is conditionally independent of the covariate vector given a suitable linear combination of the covariates. This convenient dimension-reduction approach is a natural compromise between the parametric and fully nonparametric regressions or models for conditional laws. Several estimation techniques for single-index regression are available and commonly used in applications. Most of them concern the mean or quantile regression, only few methods were proposed for conditional law modeling. In this paper, we propose a novel kernel-based semiparametric estimation approach based on the minimization of a quadratic form. The new approach is convenient for the single-index approach in mean regression and conditional law modeling. We compare the performances of our new estimation method to existing procedures.