Superiority of the r–k Class Estimator Over Some Estimators In A Linear Model

Abstract

In regression analysis, to overcome the problem of multicollinearity, the r − k class estimator is proposed as an alternative to the ordinary least squares estimator which is a general estimator including the ordinary ridge regression estimator, the principal components regression estimator and the ordinary least squares estimator. In this article, we derive the necessary and sufficient conditions for the superiority of the r − k class estimator over each of these estimators under the Mahalanobis loss function by the average loss criterion. Then, we compare these estimators with each other using the same criterion. Also, we suggest to test to verify if these conditions are indeed satisfied. Finally, a numerical example and a Monte Carlo simulation are done to illustrate the theoretical results.

Keywords:

• Average loss criterion
• r − k Class estimator
• Mahalanobis loss function
• Principal components regression estimator
• Ridge regression estimator

2000 Mathematics Subject Classification:

• 62J05
• 62J07

View correction statement:

Erratum

Acknowledgments

This research was supported by Çukurova University Academic Research Projects under project number FEF-2008D17. The first author was supported by the TUBITAK-BIDEB.