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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 687151, 11 pages
http://dx.doi.org/10.1155/2013/687151
Research Article

Remodeling and Estimation for Sparse Partially Linear Regression Models

1Shandong University Qilu Securities Institute for Financial Studies and School of Mathematical Science, Shandong University, Jinan 250100, China
2Supercomputing Center, Shandong Computer Science Center, Jinan 250014, China
3College of Mathematics Science, Shandong Normal University, Jinan 250014, China

Received 11 October 2012; Accepted 14 December 2012

Academic Editor: Xiaodi Li

Copyright © 2013 Yunhui Zeng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.