Feature screening for multi-response ultrahigh-dimensional linear models by empirical likelihood

Abstract

This paper proposes a new feature screening method for the multi-response ultrahigh-dimensional linear model by empirical likelihood. Through a multivariate moment condition, the empirical likelihood induced ranking statistics can exploit the joint effect among responses, and thus result in a much better screening performance than the methods only considering the responses individually. Additionally, the new screening method is also extended to a conditional version so that it can recover the hidden predictors which are easily missed by the unconditional method. The sure screening 性质 of the newly proposed method and its corresponding conditional method are proved. Finally, both the numerical studies and the real data analysis are provided to illustrate the effectiveness of the proposed methods.