Ultrahigh dimensional feature screening via projection

This work is concerned with feature screening for linear model with multivariate responses and ultrahigh dimensional covariates. Instead of utilizing the correlation between every response and covariate, the linear space spanned by the multivariate responses is considered in this paper. Based on the projection theory, each covariate is projected on the linear space spanned by the multivariate responses, and a new screening procedure called projection screening (PS) is proposed. The sure screening and ranking consistency properties are established under some regular conditions. To solve some difficulties in marginally feature screening for linear model and enhance the screening performance of the proposed procedure, an iterative projection screening (IPS) procedure is constructed. The finite sample properties of the proposed procedure are assessed by Monte Carlo simulation studies and a real-life data example is analysed.