Ultra-high Dimensional Variable Screening via Density Weighted Variance

Density Weighted Variance (DWV), a novel model-free feature screening criterion is proposed for mean regression with ultrahigh-dimensional covariates. Compared with existing model free screening criteria, DWV criterion possesses faster convergence rate for inactive co-varieties and is as same convergence rate as most existing variable screening procedures for active covariates. Furthermore, DWV criterion is extended to quintile regression and multiple response regression setting. Finally, numerical simulations and a real data analysis are conducted to show the finite sample performance of the proposed methods.