Performance of the principal component two-parameter estimator in misspecified linear regression model

ABSTRACT

In this article, we consider the performance of the principal component two-parameter estimator in situation of multicollinearity for misspecified linear regression model where misspecification is due to omission of some relevant explanatory variables. The conditions of superiority of the principal component two-parameter estimator over some estimators under the Mahalanobis loss function by the average loss criterion are derived. Furthermore, a real data example and a Monte Carlo simulation study are provided to illustrate some of the theoretical results.

KEYWORDS:

• Average loss criterion
• Mahalanobis loss function
• Misspecification
• Multicollinearity
• Principal component two-parameter estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J05
• 62J07

Acknowledgments

The author wishes to thank the referees and the editor for their helpful suggestions and comments that helped to improve the quality and presentation of this article.

Funding

This work was supported by the National Science Foundation of China (Grant No. 11501254), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20140521), and the Jiangsu University youth backbone teacher training project.