Feature screening for multi-response linear models by empirical likelihood

TL;DR

This paper introduces a novel feature screening method for multi-response ultrahigh dimensional linear models using empirical likelihood, effectively capturing joint response effects and heterogeneity in error variance.

Contribution

It develops a new empirical likelihood-based screening method that improves detection of relevant features in multi-response models and extends to a conditional version for hidden predictor recovery.

Findings

Outperforms existing methods in simulations and real data.

Proves sure screening property under model assumptions.

Effectively captures joint response effects and heterogeneity.

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 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.