title: Robust estimation for partially linear models with large-dimensional covariates.
abstract: We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of [Formula: see text], wherenis the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.
authors: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China ; The Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai 200433, China.
authors: LiPing
authors: L
authors: Zhu
authors: Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, PA 16802, USA.
authors: RunZe
authors: R
authors: Li
authors: School of Mathematical Science, Capital Normal University, Beijing 100037, China.
authors: HengJian
authors: H
authors: Cui
keywords: partially linear models; robust model selection; semiparametric models; smoothly clipped absolute deviation (SCAD)