Fused mean-variance filter for feature screening

A new model-free screening approach called as the slicing fused mean-variance filter is proposed for ultrahigh dimensional data analysis. The new method has the following merits: (i) its implementation does not require specifying a regression form of predictors and response variables; (ii) it can deal with various types of covariates and response variables including continuous, discrete and categorical variables; (iii) it works well even when the covariates/random errors are heavy-tailed, or the predictors are strongly correlated, or there are outliers; (iv) it is unsensitive to the slicing scheme. Under some regularity conditions, the sure screening and ranking consistency properties are established for the proposed procedure without assuming any moment conditions on the predictors. Simulation studies are conducted to investigate the finite sample performance of the proposed procedure. A real data example is illustrated to the proposed procedure.