Variable Selection and Estimation in High-Dimensional Partially Linear Models

In this paper, we propose an approach for achieving simultaneously variable selection and estimation for the linear and nonparametric components in high-dimensional partially linear models. We use Dantzig selector, applied to the linear part and various derivatives of nonparametric component, to achieve sparsity in the linear part and produce nonparametric estimators. Non-asymptotic theoretical bounds on the estimator error are obtained. The finite sample properties of the proposed approach are investigated through a simulation study