Robust estimation for partially linear models with large-dimensional covariates

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• 作者：LiPing Zhu (1) (2)
  RunZe Li (3)
  HengJian Cui (4)
  
• 关键词：partially linear models ; robust model selection ; smoothly clipped absolute deviation (SCAD) ; semiparametric models ; 62F35 ; 62G35
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2013
• 出版时间：October 2013
• 年：2013
• 卷：56
• 期：10
• 页码：2069-2088
• 全文大小：381KB
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• 作者单位：LiPing Zhu (1) (2)
  RunZe Li (3)
  HengJian Cui (4)
  
  1. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, 200433, China
  2. The Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai, 200433, China
  3. Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, PA, 16802, USA
  4. School of Mathematical Science, Capital Normal University, Beijing, 100037, China
  
• ISSN：1869-1862

文摘

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 $o\left( {\sqrt n } \right)$ , 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.