Robust variable screening for regression using factor profiling

TL;DR

This paper introduces a robust variable screening method for high-dimensional regression that models predictor correlations with latent factors and uses robust estimators to handle outliers, improving performance on contaminated data.

Contribution

It proposes a novel robust screening approach combining factor profiling with outlier-resistant estimators for high-dimensional regression.

Findings

Outperforms nonrobust methods on contaminated data

Effective in handling outliers in predictor variables

Maintains good performance on clean data

Abstract

Sure Independence Screening is a fast procedure for variable selection in ultra-high dimensional regression analysis. Unfortunately, its performance greatly deteriorates with increasing dependence among the predictors. To solve this issue, Factor Profiled Sure Independence Screening (FPSIS) models the correlation structure of the predictor variables, assuming that it can be represented by a few latent factors. The correlations can then be profiled out by projecting the data onto the orthogonal complement of the subspace spanned by these factors. However, neither of these methods can handle the presence of outliers in the data. Therefore, we propose a robust screening method which uses a least trimmed squares method to estimate the latent factors and the factor profiled variables. Variable screening is then performed on factor profiled variables by using regression MM-estimators. Different types of outliers in this model and their roles in variable screening are studied. Both simulation studies and a real data analysis show that the proposed robust procedure has good performance on clean data and outperforms the two nonrobust methods on contaminated data.