The small sample properties of the restricted principal component regression estimator in linear regression model. Issue 4 (16th February 2017)

• Record Type: Journal Article
• Authors: Wu, Jibo
• Is Part Of: Communications in statistics. Volume 46:Issue 4(2017)
• Page Start: 1661
• Page End: 1667
• Publication Date: 2017-02-16
• Subjects: Pitman's closeness criterion -- Principal components regression estimator -- Restricted principal components regression estimator; 62J05; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1024867
• Languages: English
• ISSNs: 0361-0926

Abstract

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.