Robust Sure Independence Screening for Non-polynomial dimensional Generalized Linear Models

TL;DR

This paper introduces a robust variable screening method for high-dimensional generalized linear models using minimum density power divergence estimators, demonstrating stability under noise and contamination.

Contribution

It proposes a novel robust screening procedure based on MDPDEs for GLMs, with theoretical guarantees and extensions for conditional screening in high-dimensional settings.

Findings

Method performs well under contaminated data.

Proven to have the sure screening property.

Validated through numerical studies and real data.

Abstract

We consider the problem of variable screening in ultra-high dimensional generalized linear models (GLMs) of non-polynomial orders. Since the popular SIS approach is extremely unstable in the presence of contamination and noise, we discuss a new robust screening procedure based on the minimum density power divergence estimator (MDPDE) of the marginal regression coefficients. Our proposed screening procedure performs well under pure and contaminated data scenarios. We provide a theoretical motivation for the use of marginal MDPDEs for variable screening from both population as well as sample aspects; in particular, we prove that the marginal MDPDEs are uniformly consistent leading to the sure screening property of our proposed algorithm. Finally, we propose an appropriate MDPDE based extension for robust conditional screening in GLMs along with the derivation of its sure screening property. Our proposed methods are illustrated through extensive numerical studies along with an interesting real data application.