The small sample properties of the restricted principal component regression estimator in linear regression model

ABSTRACT

In regression analysis, to deal with the problem of multicollinearity, the restricted principal components regression estimator is proposed. In this paper, we compared the restricted principal components regression estimator, the principal components regression estimator, and the ordinary least-squares estimator with each other under the Pitman's closeness criterion. We showed that the restricted principal components regression estimator is always superior to the principal components regression estimator, under certain conditions the restricted principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion and under certain conditions the principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion.

KEYWORDS:

• Pitman's closeness criterion
• Principal components regression estimator
• Restricted principal components regression estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J05

Acknowledgments

The author is highly obliged to the editors and the reviewers for the comments and suggestions which improved the paper in its present form.

Funding

This work was supported by the National Natural Science Foundation of China [No. 11501072], the Natural Science Foundation Project of CQ CSTC [No. cstc2015jcyjA00001], and the Scientific and Technological Research Program of Chongqing Municipal Education Commission [No. KJ1501114].