Development and evaluation of new two-parameter ridge estimators for handling multicollinearity: simulation and applications

Multicollinearity refers to the presence of high correlation among the predictors. This issue is addressed by using the ridge regression approach, which requires selecting an optimal value of the ridge parameter to achieve an appropriate bias–variance trade-off. There exist various one-parameter and two-parameter methods of estimating the ridge parameter. In this study, several new two-parameter ridge estimators are developed to deal with the problem of multicollinearity. The performance of the proposed estimators is examined using Monte Carlo simulations and real-life data analyses based on the mean squared error (MSE) criterion. The simulation and real-life data analyses demonstrate the significant improvement of the newly proposed two-parameter ridge estimators in handling multicollinearity, in terms of mean squared error (MSE). For the majority of simulation scenarios, the proposed MQW3 estimator outperforms all other estimators considered in the study. Further, the real-data analyses on gasoline consumption and sports datasets also support simulation findings.