Improved ridge estimators in a linear regression model

Abstract

In this paper, the notion of the improved ridge estimator (IRE) is put forward in the linear regression model y=X β+e. The problem arises if augmenting the equation 0=c′α+ε instead of 0=C α+ϵ to the model. Three special IREs are considered and studied under the mean-squared error criterion and the prediction error sum of squares criterion. The simulations demonstrate that the proposed estimators are effective and recommendable, especially when multicollinearity is severe.

Keywords:

• linear regression
• improved ridge estimator
• singular value decomposition
• MSE
• PRESS

MSC 2010 :

• 62J05

Acknowledgements

The authors are very grateful to the referees for valuable comments and constructive suggestions which result in the present version of the article. They also give thanks to Mr Ming-Xing Ma for his some motivated aspects when the original version of this paper was prepared. The research was sponsored by the Qing Lan Project from Jiangsu province and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 11KJB110001).