Model-Free Conditional Feature Screening with Exposure Variables

TL;DR

This paper introduces a model-free conditional feature screening method that identifies significant predictors in high-dimensional data, accounting for exposure variables, heteroscedasticity, and outliers, with proven theoretical properties and practical validation.

Contribution

It proposes a novel, model-free screening approach based on conditional correlation with exposure variables, applicable to diverse models and robust to outliers.

Findings

Method achieves sure screening property under mild conditions.

Simulation studies demonstrate strong finite sample performance.

Application to breast cancer data validates practical utility.

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.