Analyzing the Impact of Robust Covariance Estimators in Managing Multicollinearity and Outlier Influence

Posted: Mar 11, 2019

• Logan Rivera
• Madeline Cooper
• Marcus Ward

Abstract

The persistent challenges of multicollinearity and outlier influence represent two of the most fundamental obstacles in statistical modeling and machine learning applications. Multicollinearity, characterized by high intercorrelations among predictor variables, undermines the stability and interpretability of parameter estimates, while outliers can dramatically distort statistical inferences and model predictions. Despite their frequent co-occurrence in real-world datasets, these phenomena have traditionally been addressed through separate analytical frameworks that often operate at cross-purposes. This research introduces a novel methodological framework that bridges this gap by integrating robust covariance estimation directly into multicollinearity diagnostics. We propose that robust estimators—specifically Minimum Covariance Determinant (MCD), Minimum Volume Ellipsoid (MVE), and S-estimators—offer a mathematically coherent solution to the dual challenges of multicollinearity and outlier influence. Our approach reconceptualizes multicollinearity not merely as a property of the data generating process but as a characteristic that must be assessed through outlier-resistant lenses to ensure diagnostic reliability.