Robust Kibria Estimators for Mitigating Multicollinearity and Outliers in a Linear Regression Model

In the presence of multicollinearity, the ordinary least squares (OLS) estimators, aside from BLUE (best linear unbiased estimator), lose efficiency and fail to achieve minimum variance. In addition, these estimators are highly sensitive to outliers in the response direction. To overcome these limitations, robust estimation techniques are often integrated with shrinkage methods. This study proposes a new class of Kibria Ridge M-estimators specifically developed to simultaneously address multicollinearity and outlier contamination. A comprehensive Monte Carlo simulation study is conducted to evaluate the performance of the proposed and existing estimators. Based on the mean squared error criterion, the proposed Kibria Ridge M-estimators consistently outperform the traditional ridge-type estimators under varying parameter settings. Furthermore, the practical applicability and superiority of the proposed estimators are validated using the Tobacco and Anthropometric datasets. Overall, the new proposed estimators demonstrate good performance, offering robust and efficient alternatives for regression modeling in the presence of multicollinearity and outliers.