  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 performance than the methods considering responses individually.
More importantly, by the use of empirical likelihood, the new method adapts to
the heterogeneity in the conditional variance of random error. The sure
screening property of the newly proposed method is proved with the model size
controlled within a reasonable scale. 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
corresponding theoretical properties are also provided. Finally, both numerical
studies and real data analysis are provided to illustrate the effectiveness of
the proposed methods.
