Model-Free Conditional Feature Screening with Exposure Variables

Abstract

In high dimensional analysis, effects of explanatory variables on responses sometimes rely on certain exposure variables, such as time or environmental factors. In this paper, to characterize the importance of each predictor, we utilize its conditional correlation given exposure variables with the empirical distribution function of response. A model-free conditional screening method is subsequently advocated based on this idea, aiming to identify significant predictors whose effects may vary with the exposure variables. The proposed screening procedure is applicable to any model form, including that with heteroscedasticity where the variance component may also vary with exposure variables. It is also robust to extreme values or outlier. Under some mild conditions, we establish the desirable sure screening and the ranking consistency properties of the screening method. The finite sample performances are illustrated by simulation studies and an application to the breast cancer dataset.