Simultaneously Addressing Collinearity and Outliers: A Robust Two-Parameter Estimation Approach

Abstract

Multicollinearity and outliers remain two major challenges in linear regression modeling, often occurring simultaneously in practical applications and leading to instability, inflated variance, and unreliable inference. Although shrinkage estimators such as ridge and Liu estimators effectively address multicollinearity, but are still sensitive to outliers. Conversely, robust estimators mitigate the influence of outliers but do not adequately resolve collinearity. This study proposes a new robust two-parameter shrinkage estimator (Rprop1) designed to simultaneously handle multicollinearity and outliers within the classical linear regression framework. The estimator is derived in canonical form, and its statistical properties are established through mean squared error (MSE) analysis. A comprehensive Monte Carlo simulation study is conducted across varying sample sizes, error variances, correlation levels, numbers of explanatory variables, and outlier magnitudes. The performance of the proposed estimator is compared with existing robust and shrinkage-based estimators, including robust ridge, robust Liu, and robust Kibra Lukman estimators. Simulation results consistently demonstrate that the proposed estimator achieves superior MSE performance across moderate to severe multicollinearity and outliers’ magnitudes and it’s also supported by the real life dataset. The findings suggest that the proposed method provides a more stable and efficient alternative for regression modeling in the presence of simultaneous collinearity and outliers.