Consistent covariate selection and post model selection inference in semiparametric regression

Abstract

This paper presents a model selection technique of estimation in semiparametric regression models of the type $Y_{i}={\beta}^{\prime}\underline{X}_{i}+f(T_{i})+W_{i}$ , i=1,…,n. The parametric and nonparametric components are estimated simultaneously by this procedure. Estimation is based on a collection of finite-dimensional models, using a penalized least squares criterion for selection. We show that by tailoring the penalty terms developed for nonparametric regression to semiparametric models, we can consistently estimate the subset of nonzero coefficients of the linear part. Moreover, the selected estimator of the linear component is asymptotically normal.