Robust group variable screening based on maximum Lq-likelihood estimation.

Variable screening plays an important role in ultra-high-dimensional data analysis. Most of the previous analyses have focused on individual predictor screening using marginal correlation or other rank-based techniques. When predictors can be naturally grouped, the structure information should be incorporated while applying variable screening. This study presents a group screening procedure that is based on maximum Lq-likelihood estimation, which is being increasingly used for robust estimation. The proposed method is robust against data contamination, including a heavy-tailed distribution of the response and a mixture of observations from different distributions. The sure screening property is rigorously established. Simulations demonstrate the competitive performance of the proposed method, especially in terms of its robustness against data contamination. Two real data analyses are presented to further illustrate its performance.