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Journal of Applied Mathematics
Volume 2013, Article ID 858794, 7 pages
http://dx.doi.org/10.1155/2013/858794
Research Article

On the Performance of Principal Component Liu-Type Estimator under the Mean Square Error Criterion

Jibo Wu1,2

1School of Mathematics and Finances, Chongqing University of Arts and Sciences, Chongqing 402160, China
2Department of Mathematics and KLDAIP, Chongqing University of Arts and Sciences, Chongqing 402160, China

Received 10 October 2013; Accepted 12 November 2013

Academic Editor: Renat Zhdanov

Copyright © 2013 Jibo Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Wu (2013) proposed an estimator, principal component Liu-type estimator, to overcome multicollinearity. This estimator is a general estimator which includes ordinary least squares estimator, principal component regression estimator, ridge estimator, Liu estimator, Liu-type estimator, class estimator, and class estimator. In this paper, firstly we use a new method to propose the principal component Liu-type estimator; then we study the superior of the new estimator by using the scalar mean squares error criterion. Finally, we give a numerical example to show the theoretical results.