Robust estimation for partially linear models with large-dimensional covariates  

作　　者：ZHU LiPing LI RunZe CUI HengJian 

机构地区：[1]School of Statistics and Management, Shanghai University of Finance and Economics [2]The Key Laboratory of Mathematical Economics (SUFE), Ministry of Education [3]Department of Statistics and The Methodology Center, The Pennsylvania State University,University Park [4]School of Mathematical Science, Capital Normal University

出　　处：《Science China Mathematics》2013年第10期2069-2088,共20页中国科学：数学（英文版）

基　　金：supported by National Institute on Drug Abuse(Grant Nos.R21-DA024260 and P50-DA10075);National Natural Science Foundation of China(Grant Nos.11071077,11371236,11028103,11071022 and 11028103);Innovation Program of Shanghai Municipal Education Commission;Pujiang Project of Science and Technology Commission of Shanghai Municipality(Grant No.12PJ1403200);Program for New Century Excellent Talents,Ministry of Education of China(Grant No.NCET-12-0901)

摘　　要：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 o（√n）, where n is 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.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 nonconcave 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 o(n1/2), where n is 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 fnite-sample performance of the proposed procedures.

关 键 词：partially linear models robust model selection smoothly clipped absolute deviation （SCAD） semiparametric models 

分 类 号：O212.1[理学—概率论与数理统计] TP391.41[理学—数学]