How to Make Model‐free Feature Screening Approaches for Full Data Applicable to the Case of Missing Response?
针对响应变量缺失的高维数据，提出了两种新方法，通过借用缺失指示信息，使任何适用于完整数据的特征筛选方法都能处理缺失响应问题，并证明了其筛选一致性。
Abstract 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.