Fused Mean-variance Filter for Feature Screening

Abstract: This paper proposes a novel model-free screening procedure for ultrahigh dimensional data analysis. By utilizing slicing technique which has been successfully ap- plied to continuous variables, we construct a new index called the fused mean-variance for feature screening. This method has the following merits: (i) it is model-free, i.e., without specifying regression form of predictors and response variable; (ii) it can be used to analyze various types of variables including discrete, categorical and continuous vari- ables; (iii) it still works well even when the covariates/random errors are heavy-tailed or the predictors are strongly dependent. Under some regularity conditions, we establish the sure screening and rank consistency. Simulation studies are conducted to assess the performance of the proposed approach. A real data is used to illustrate the proposed method.