Comparative analysis of robust ridge M-estimators using simulation and empirical studies

Abstract

ABSTRACT In the recent studies, robust biasing parameter ‘k’ has been introduced by Naz et al. (2025) to overcome the joint problem of multicollinearity and outliers in ridge regression model. However, the presence of outliers and severe multicollinearity in the data set may have some adverse effects on the Naz estimators. To overcome these challenging situations, this study introduces a novel weight base ridge M-estimators. The performance of the new estimators is evaluated through simulation study via mean squared error (MSE) criterion. The results show that new estimators has better performance than existing estimators in certain scenarios. To illustrate the simulation results, three numerical examples are presented using prediction sum of square of error (PRESS) as performance measures. Numerical examples also supports the simulation findings and shows the best performance of new estimators over Naz estimators.