Robust estimation for partially linear models with large-dimensional covariates. 2013

LiPing Zhu, and RunZe Li, and HengJian Cui
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.

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], 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.

UI MeSH Term Description Entries

Related Publications

LiPing Zhu, and RunZe Li, and HengJian Cui
March 2013, Journal of the Royal Statistical Society. Series B, Statistical methodology,
LiPing Zhu, and RunZe Li, and HengJian Cui
May 2008, Journal of multivariate analysis,
LiPing Zhu, and RunZe Li, and HengJian Cui
January 2017, Journal of inequalities and applications,
LiPing Zhu, and RunZe Li, and HengJian Cui
December 2016, Statistics in medicine,
LiPing Zhu, and RunZe Li, and HengJian Cui
December 2008, Australian & New Zealand journal of statistics,
LiPing Zhu, and RunZe Li, and HengJian Cui
March 2009, Annals of the Institute of Statistical Mathematics,
LiPing Zhu, and RunZe Li, and HengJian Cui
December 2020, Statistics in medicine,
LiPing Zhu, and RunZe Li, and HengJian Cui
March 2007, Biometrika,
LiPing Zhu, and RunZe Li, and HengJian Cui
June 2021, Psychometrika,
LiPing Zhu, and RunZe Li, and HengJian Cui
June 2010, Journal of the American Statistical Association,
Copied contents to your clipboard!