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Estimation and variable selection in partial linear single index models with error-prone linear covariates |
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| Authors: | Jun Zhang Xiaoguang Wang Yao Yu Yujie Gai |
| Affiliation: | 1. Shen Zhen-Hong Kong Joint Research Centre for Applied Statistical Sciences, College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, People's Republic of Chinazhangjunstat@gmail.com;3. School of Mathematical Sciences, Dalian University of Technology, Dalian, People's Republic of China;4. Department of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry, Rochester, NY, USA;5. School of Statistics, Central University of Finance and Economics, Beijing, People's Republic of China |
| Abstract: | We study the estimation and variable selection for a partial linear single index model (PLSIM) when some linear covariates are not observed, but their ancillary variables are available. We use the semiparametric profile least-square based estimation procedure to estimate the parameters in the PLSIM after the calibrated error-prone covariates are obtained. Asymptotic normality for the estimators are established. We also employ the smoothly clipped absolute deviation (SCAD) penalty to select the relevant variables in the PLSIM. The resulting SCAD estimators are shown to be asymptotically normal and have the oracle property. Performance of our estimation procedure is illustrated through numerous simulations. The approach is further applied to a real data example. |
| Keywords: | ancillary variables error-prone local linear smoothing profile least square method SCAD single-index |