Pooled marginal slicing approach via SIR _α with discrete covariables

In this paper, we consider a semiparametric regression model involving both p-dimensional quantitative covariable X and categorical predictor Z, and including a dimension reduction of X via K indices Xβ _k . The dependent variable Y can be real or q-dimensional. We propose an approach based on SIR _α and pooled marginal slicing methods in order to estimate the space spanned by the β _k 's. We establish n} -consistency of the proposed estimator. Simulation studies show the numerical qualities of our estimator.