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The Scientific World Journal
Volume 2014 (2014), Article ID 231506, 6 pages
http://dx.doi.org/10.1155/2014/231506
Research Article

A Stochastic Restricted Principal Components Regression Estimator in the Linear Model

Department of Statistics, Anhui Normal University, Wuhu 241000, China

Received 2 August 2013; Accepted 4 November 2013; Published 23 January 2014

Academic Editors: M. Blank, J. De Brabanter, and C. Neves

Copyright © 2014 Daojiang He and Yan 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

We propose a new estimator to combat the multicollinearity in the linear model when there are stochastic linear restrictions on the regression coefficients. The new estimator is constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator, which is called the stochastic restricted principal components (SRPC) regression estimator. Necessary and sufficient conditions for the superiority of the SRPC estimator over the OME and the PCR estimator are derived in the sense of the mean squared error matrix criterion. Finally, we give a numerical example and a Monte Carlo study to illustrate the performance of the proposed estimator.