Adaptive Penalized Regression for High-Efficiency Estimation in Correlated Predictor Settings: A Data-Driven Shrinkage Approach

Penalized regression estimators have become widely adopted alternatives to ordinary least squares while analyzing collinear data, despite introducing some bias. However, existing penalized methods lack universal superiority across diverse data conditions. To address this limitation, we propose a novel adaptive ridge estimator that automatically adjusts its penalty structure based on key data characteristics: (1) the degree of predictor collinearity, (2) error variance, and (3) model dimensionality. Through comprehensive Monte Carlo simulations and real-world applications, we evaluate the estimator’s performance using mean squared error (MSE) as our primary criterion. Our results demonstrate that the proposed method consistently outperforms existing approaches across all considered scenarios, with particularly strong performance in challenging high-collinearity settings. The real-data applications further confirm the estimator’s practical utility and robustness.