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.
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