The presence of outlier observations may lead to misleading results in variable screening problems. To address this issue, this paper presents a new robust variable screening method using the L1 loss and the Huber loss. As an extension, we also develop an effective iterative procedure to improve the finite sample performance of the presented method. The effectiveness of the proposed methods is illustrated through simulation studies and real data analysis to show their capabilities. Numerical studies show that the proposed methods work well with ultrahigh-dimensional data sets, which may contain outliers, and perform better than some competing methods.
Mohammad Kazemi (Sat,) studied this question.