College of Statistics and Data Science, Faculty of Science, Beijing University of Technology, Beijing, 100124, China; Beijing Institute of Computer Technology and Applications, Beijing, 100854, China; School of Science, Xuchang University, Xuchang, 461000, China
In this paper, we consider the ultrahigh dimensional partially linear model, in which the dimension of the parametric vector is exponential order of the sample size. Based on profile least squares and regularization after retention method, we propose a new method to perform variable selection for the ultrahigh dimensional partially linear model. Under certain regularity conditions, it is proved that the estimator achieves sign consistency. Compared with Lasso, SIS-Lasso and adaptive Lasso, it is found that the proposed method is better in terms of recovering the coefficient sign of linear part through the numerical simulation and real data analysis.
杨鑫; 李冰月; 田萍. 超高维部分线性模型的PRAR变量选择[J]. 应用概率统计, 2021, 37(6): 551-568.
YANG Xin; LI Bingyue; TIAN Ping. partially linear model; variable selection;high-dimensional data; Lasso; sign consistency; regularization afterretention. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2021, 37(6): 551-568.
