Shrinkage Approaches for Ridge-Type Estimators Under Multicollinearity

Multicollinearity is a common issue in regression analysis that occurs when some predictor variables are highly correlated, leading to unstable least squares estimates of model parameters. Various estimation strategies have been proposed to address this problem. In this study, we enhance a ridge-type estimator by incorporating pretest and shrinkage techniques. We conducted an analytical comparison to evaluate the performance of the proposed estimators in terms of bias, quadratic risk, and numerical performance using both simulated and real data. Additionally, we assessed several penalization methods and three machine-learning algorithms to facilitate a comprehensive comparison. Our results demonstrate that the proposed estimators outperform the standard ridge-type estimator with respect to mean squared error in simulated data and mean squared prediction error in real data applications.