Mitigating multicollinearity and outliers in regression: comparison of some new and old robust ridge M-estimators

作者：Danish Wasim, Qamruz Zaman, Mansoor Ahmad, B. M. Golam Kibria · 发表于：Journal of Statistical Computation and Simulation · 年份：2025 · DOI：10.1080/00949655.2025.2538110 · 被引用次数：3 · 研究领域：Advanced Statistical Methods and Models、Advanced Statistical Process Monitoring、Statistical Methods and Inference

In the multiple linear regression model (MLRM), ordinary least squares and ridge regression (RR) estimates often fail due to multicollinearity and outliers in the y-direction. To address these issues, robust ridge M-estimators offer robustness against outliers and handle multicollinearity. This work presents new robust ridge M-estimators that utilize the MSE criterion and outperform previous approaches. A Monte Carlo simulation study has been conducted to assess the efficiency of the newly proposed estimator. Based on this simulation study, it is suggested to use a robust ridge M-estimator that automatically adjusts to degrees of multicollinearity and noise. This estimator performs well in simulations involving significant error variance, y-direction outliers and strong multicollinearity. The estimator's efficiency is demonstrated for both normal and heavy-tailed error distributions, and an empirical example confirms its effectiveness.