How to Make Model-free Feature Screening Approaches for Full Data Applicable to the Case of Missing Response?

It is quite a challenge to develop model-free feature screening approaches for missing response problems because the existing standard missing data analysis methods cannot be applied directly to high dimensional case. This paper develops some novel methods by borrowing information of missingness indicators such that any feature screening procedures for ultrahigh-dimensional covariates with full data can be applied to missing response case. The first method is the so-called missing indicator imputation screening, which is developed by proving that the set of the active predictors of interest for the response is a subset of the active predictors for the product of the response and missingness indicator under some mild conditions. As an alternative, another method called Venn diagram-based approach is also developed. The sure screening property is proven for both methods. It is shown that the complete case analysis can also keep the sure screening property of any feature screening approach with sure screening property.