Abstract
In this study, we introduce three new shrinkage parameters for ridge regression, which dynamically adjust the ridge penalty based on the properties of the data, particularly the multicollinearity structure. Using these new parameters, we develop three ridge condition-adjusted estimators (CAREs), referred to as CARE1, CARE2, and CARE3, which specifically designed to enhance predictive accuracy in datasets with significant multicollinearity and high error variance. The performance of the developed shrinkage estimators is rigorously evaluated through extensive simulation studies, using the Mean Square Error (MSE) criterion for accuracy assessment. The simulation results reveal that our proposed estimators consistently outperform existing estimators under different scenarios. We also apply these estimators to a real-world dataset to demonstrate their practical effectiveness, thereby showcasing their applicability in real-life data analysis. The real-world application further validates their practical utility for accurate prediction and model stability in complex scenarios in which the CARE3 emerged as the best-performing shrinkage estimator.