Sparse Robust Weighted Expectile Screening for Ultra-High-Dimensional Data

This paper investigates robust feature screening for ultra-high dimensional data in the presence of outliers and heterogeneity. Considering the susceptibility of likelihood methods to outliers, we propose a Sparse Robust Weighted Expectile Regression (SRoWER) method that combines the L2E criterion with expectile regression. By utilizing the IHT algorithm, our method effectively incorporates correlations of covariates and enables joint feature screening. The proposed approach demonstrates robustness against heavy-tailed errors and outliers in data. Simulation studies and a real data analysis are provided to demonstrate the superior performance of the SRoWER method when dealing with outlier-contaminated explanatory variables and/or heavy-tailed error distributions.