Contraction Ridge Estimator: Simulation and Application to Economic Data
摘要
This paper introduces a novel regularization technique known as the Contraction Ridge estimator (CRidge), designed to address the limitations of traditional Least Squares (LS) and other biased estimation methods such as Ridge, Liu, Kibria-Lukman (KL), and Contraction Least Squares (COLS) estimators, particularly in the presence of multicollinearity. The proposed estimator modifies the COLS by integrating ridge regression, enhancing its numerical stability and performance in high-dimensional and highly collinear settings. Theoretical comparisons are presented, establishing conditions under which CRidge outperforms other estimators based on Mean Squared Error Matrix (MSEM) and Scalar Mean Squared Error (SMSE) criteria. A comprehensive Monte Carlo simulation study further validates the theoretical findings, demonstrating the superiority of CRidge over LS, Ridge, Liu, KL, and COLS estimators in various scenarios, including different levels of multicollinearity, sample sizes, and noise levels. In addition, an empirical application using the electricity data illustrates the practical utility of the CRidge estimator. The results show that CRidge consistently achieves lower SMSE, Prediction Mean Squared Error (PMSE) and Prediction Mean Absolute Error (PMAE) compared to other methods, indicating its robustness and effectiveness for regression analysis under multicollinearity. The contraction ridge estimator is recommended as a reliable and efficient tool to improve estimation accuracy and prediction stability in complex regression problems.