Performance of some robust improved Kibria-Lukman M-estimators for linear regression model in presence of multicollinearity and outliers

Multicollinearity often undermines the performance of the ordinary least squares (OLS) estimator in linear regression models. While ridge-type estimators have been developed to overcome this issue, their efficiency deteriorates in the presence of outliers. To address this limitation, this study introduces a new class of robust improved Kibria–Lukman M-estimators (MKLM), designed to handle both multicollinearity and contamination in the response variable simultaneously. Through extensive Monte Carlo simulations, the proposed MKLM estimators demonstrate superior performance in terms of mean squared error (MSE) compared to existing ridge and robust ridge-type estimators. A real data example further confirms the effectiveness of the MKLM2 estimator as the most efficient among all considered methods.