Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2012), Article ID 687151, 11 pages.
Remodeling and Estimation for Sparse Partially Linear Regression Models
When the dimension of covariates in the regression model is high, one usually uses a submodel as a working model that contains significant variables. But it may be highly biased and the resulting estimator of the parameter of interest may be very poor when the coefficients of removed variables are not exactly zero. In this paper, based on the selected submodel, we introduce a two-stage remodeling method to get the consistent estimator for the parameter of interest. More precisely, in the first stage, by a multistep adjustment, we reconstruct an unbiased model based on the correlation information between the covariates; in the second stage, we further reduce the adjusted model by a semiparametric variable selection method and get a new estimator of the parameter of interest simultaneously. Its convergence rate and asymptotic normality are also obtained. The simulation results further illustrate that the new estimator outperforms those obtained by the submodel and the full model in the sense of mean square errors of point estimation and mean square prediction errors of model prediction.
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 687151, 11 pages.
First available in Project Euclid: 26 February 2014
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Zeng, Yunhui; Wang, Xiuli; Lin, Lu. Remodeling and Estimation for Sparse Partially Linear Regression Models. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 687151, 11 pages. doi:10.1155/2013/687151. https://projecteuclid.org/euclid.aaa/1393450539