Weighted penalized m-estimators in robust ridge regression: an application to gasoline consumption data

The OLS and ridge regression (RR) estimators are adversely affected, when the problem of multicollinearity and y-direction outliers occur together. The robust ridge regression with penalized parameters offers biased estimators with lower variance than OLS and RR. The optimal penalized parameter value is crucial for balancing variance and bias. This study proposes three new weighted robust penalized M-estimators to address both multicollinearity and y-direction outliers. Their performance is evaluated against OLS, RR and existing penalized M-estimators using Monte Carlo simulations based on mean squared error (MSE). The new estimators exhibit lower MSE in the presence of multicollinearity and y-direction outliers. A real data application on gasoline consumption demonstrates the superior performance of the new estimators.