Robust sure independence screening for ultrahigh dimensional non-normal data

Abstract

Sure independence screening (SIS) has been proposed to reduce the ultrahigh dimensionality down to a moderate scale and proved to enjoy the sure screening property under Gaussian linear models. However, the observed response is often skewed or heavy-tailed with extreme values in practice, which may dramatically deteriorate the performance of SIS. To this end, we propose a new robust sure independence screening (RoSIS) via considering the correlation between each predictor and the distribution function of the response. The proposed approach contributes to the literature in the following three folds: First, it is able to reduce ultrahigh dimensionality effectively. Second, it is robust to heavy tails or extreme values in the response. Third, it possesses both sure screening property and ranking consistency property under milder conditions. Furthermore, we demonstrate its excellent finite sample performance through numerical simulations and a real data example.