Weighted ridge and Liu estimators for linear regression model

In linear regression model, ridge regression and two-parameter Liu estimator (LE) are the most widely used methods in recent decade to overcome the problem of multicollinearity especially for ill conditioned cases. In this article, we propose new weighted ridge and Liu estimators which remain positive for each level of multicollinearity and also give smaller mean squared error (MSE) than the existing ridge regression and existing Liu estimators. In addition, a new adaptive LE for k which accounts for the error variance is also proposed to assess the ill condition cases. Furthermore, new weighted ridge estimator of Kibria arithmetic mean method and two parameter Liu estimator with Liu method are also proposed. Extensive Monte-Carlo simulations are used to evaluate the performance of proposed estimators. Based on MSE criterion, the proposed estimators perform better than the existing estimators in many situations including severe multicollinearity and small signal-to- noise ratio. Two real life applications are also provided to illustrate the usefulness of new estimators.

Automated summary

New weighted ridge and Liu estimators are proposed in this article to overcome the problem of multicollinearity, and they perform better than existing methods in terms of performance. The effectiveness and practicality of these methods are validated through Monte-Carlo simulations and real-life applications.