| Institution: | 1. Department of Statistics, Yunnan University, Kunming, Yunnan, 650504 P.R. China
School of Statistics, Qufu Normal University, Qufu, Shandong, 273165 P.R. China;2. International Business College and Institute of Supply Chain Analytics, Dongbei University of Finance and Economics, Dalian, Liaoning, 116025 P.R. China;3. School of Statistics, Qufu Normal University, Qufu, Shandong, 273165 P.R. China |
| Abstract: | In this article, a robust variable selection procedure based on the weighted composite quantile regression (WCQR) is proposed. Compared with the composite quantile regression (CQR), WCQR is robust to heavy-tailed errors and outliers in the explanatory variables. For the choice of the weights in the WCQR, we employ a weighting scheme based on the principal component method. To select variables with grouping effect, we consider WCQR with SCAD-L2 penalization. Furthermore, under some suitable assumptions, the theoretical properties, including the consistency and oracle property of the estimator, are established with a diverging number of parameters. In addition, we study the numerical performance of the proposed method in the case of ultrahigh-dimensional data. Simulation studies and real examples are provided to demonstrate the superiority of our method over the CQR method when there are outliers in the explanatory variables and/or the random error is from a heavy-tailed distribution. |
