A nonparametric feature screening method for ultrahigh-dimensional missing response

Abstract

This paper addresses the feature screening issue for ultrahigh-dimensional data with responses missing at random. A novel nonparametric feature screening procedure is developed to identify the important features via the conditionally imputing marginal Spearman rank correlation. The proposed nonparametric screening approach has several desirable merits. First, it is nonparametric without assuming any regression form of predictors on response variable. Second, it is robust to outliers and heavy-tailed data. Third, under some regularity conditions, it is shown that the proposed feature screening procedure has the sure screening and ranking consistency properties. Simulation studies evidence that the proposed screening procedure outperforms several existing model-free screening procedures. An example taken from the microarray diffuse large-B-cell lymphoma study is used to illustrate the proposed methodologies.