Further research on the principal component two-parameter estimator in linear model

ABSTRACT

In this article, we introduce a generalized Mahalanobis loss function which can be applied to the estimator for regression coefficients whether its covariance matrix is singular or non singular. Then, we give detailed comparisons between those estimators that can be derived from the principal component two-parameter estimator under the generalized Mahalanobis loss function by the average loss criterion. Also, we obtain conditions for the superiority of one estimator over the other and propose the optimal values for ridge parameter k and Liu parameter d. Furthermore, we illustrate the theoretical results by a numerical example and a Monte Carlo simulation study.

Keywords:

• Principal component two-parameter estimator
• r − k estimator
• r − d estimator
• Generalized Mahalanobis loss function
• Average loss criterion.

Mathematics Subject Classification::

• 62J05
• 62J07

Acknowledgments

The authors are grateful to the editor, the associate editor, and the anonymous referees for their valuable comments and suggestions to improve this article.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 11171361) and Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20110191110033).