Sufficient dimension reduction and variable selection for regression mean function with two types of predictors

In this article, for the regression mean function of Y on , where Y is a scalar, is a px1 vector and W is a categorical variable, we propose a method, partial sparse MAVE, to achieve sufficient dimension reduction and variable selection on simultaneously. The method relaxes any particular distribution assumption on the model and on . We also extend this method to multivariate response of , and GPLSIM [Carroll, R.J., Fan, J., Gijbels, I., Wand, M.P., 1997. Generalized partially linear single-index models. Journal of the American Statistical Association 92, 477-489]. Simulations and a real data analysis confirm the efficacy of our method.