Robust estimation for partially linear models with large-dimensional covariates

被引:0
|
作者
ZHU LiPing [1 ,2 ]
LI RunZe [3 ]
CUI HengJian [4 ]
机构
[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
基金
中国国家自然科学基金;
关键词
partially linear models; robust model selection; smoothly clipped absolute deviation(SCAD); semiparametric models;
D O I
暂无
中图分类号
O212.1 [一般数理统计];
学科分类号
020208 ; 070103 ; 0714 ;
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 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.
引用
收藏
页码:2068 / 2068 +2070-2088
页数:20
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