Bagging-based robust ridge M-estimators in linear regression model for mitigating multicollinearity and outliers

Real-world datasets often suffer from multicollinearity and outliers, both of which severely distort the performance of conventional regression estimators such as the Ordinary Least Squares (OLS) estimator. Multicollinearity inflates the variances of the estimated coefficients, leading to unstable and unreliable inference, while the presence of outliers further increases estimation error. The present study introduces new bootstrap aggregation (bagging) based robust ridge estimators. The proposed estimators are evaluated through extensive Monte Carlo simulations under varying levels of correlation, sample sizes, error variances, and outlier proportions. The simulation findings demonstrate that, under conditions of multicollinearity along with y direction outliers, bagging-based robust ridge estimators exhibit superior performance compared to traditional robust ridge estimators. The suggested estimators are also applied to the Cauchy distribution. Ultimately, a real-world example is employed to highlight the application of the new proposed bootstrap aggregation (bagging) based robust ridge estimators.