Robust Moderately Clipped LASSO for Simultaneous Outlier Detection and Variable Selection

Outlier detection has become an important and challenging issue in high-dimensional data analysis due to the coexistence of data contamination and high-dimensionality. Most existing widely used penalized least squares methods are sensitive to outliers due to the l(2) loss. In this paper, we proposed a Robust Moderately Clipped LASSO (RMCL) estimator, that performs simultaneous outlier detection, variable selection and robust estimation. The RMCL estimator can be efficiently solved using the coordinate descent algorithm in a convex-concave procedure. Our numerical studies demonstrate that the RMCL estimator possesses superiority in both variable selection and outlier detection and thus can be advantageous in difficult prediction problems with data contamination.