Condition-index based new ridge regression estimator for linear regression model with multicollinearity

Ridge regression is employed to estimate the regression parameters while circumventing the multicollinearity among independent variables. The ridge parameter plays a vital role as it controls bias-variance tradeoff. Several methods for choosing the ridge parameter are suggested in the literature. In this paper, we suggest a new ridge estimator which is a function of condition index, number of predictors and error variance. This new proposal has the novelty to have a sort of automatic dealing with the multicollinearity level and signal-to-noise ratio. Extensive Monte Carlo simulations are performed to evaluate the performance of the proposed ridge regression estimators in various scenarios. It has been shown that the our proposed estimator outperforms the closely related estimators in terms of minimum mean squared error (MSE). Finally, two real life applications are also provided.

Automated summary

This article proposes a new ridge regression estimator that addresses the issue of multicollinearity among independent variables. The new estimator combines the condition index, number of predictors, and error variance to automatically handle the levels of multicollinearity and signal-to-noise ratio. Extensive Monte Carlo simulations demonstrate that the proposed estimator outperforms closely related estimators in terms of minimum mean squared error (MSE). Additionally, two real-life applications are provided.