New shrinkage-type estimators in a linear regression model when multicollinearity is severe

Abstract

For the linear regression model y=Xβ+e with severe multicollinearity, we put forward three shrinkage-type estimators based on the ordinary least-squares estimator including two types of independent factor estimators and a seemingly convex combination. The simulation study shows that the new estimators are not good enough when multicollinearity is mild to moderate, but perform very well when multicollinearity is severe to very severe.

Keywords:

• linear regression model
• ordinary least-squares estimator
• multicollinearity
• independent factor estimator
• combined independent factor estimator
• shrinkage-type estimator

AMS Subject classification 2010:

• 62J05
• 62J07

Acknowledgements

The authors are very grateful to the referees for their valuable suggestions and constructive criticisms as well as many detailed comments, which have resulted in the present version.

This research was sponsored by the Qing Lan Project, Jiangsu province, and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No.: 11KJB110001). The first author was partially supported by the National Natural Science Foundation of China (Grant No.: 51205151).