  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.
