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Abstract and Applied Analysis
Volume 2014, Article ID 692472, 13 pages
Research Article

The Optimal Selection for Restricted Linear Models with Average Estimator

1School of Economics, Shandong Institute of Business and Technology, Yantai, Shandong 264005, China
2School of Finance, Dongbei University of Finance and Economics, Dalian, Liaoning 116025, China

Received 5 March 2014; Revised 15 April 2014; Accepted 29 April 2014; Published 21 May 2014

Academic Editor: Qian Guo

Copyright © 2014 Qichang Xie and Meng Du. 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.


The essential task of risk investment is to select an optimal tracking portfolio among various portfolios. Statistically, this process can be achieved by choosing an optimal restricted linear model. This paper develops a statistical procedure to do this, based on selecting appropriate weights for averaging approximately restricted models. The method of weighted average least squares is adopted to estimate the approximately restricted models under dependent error setting. The optimal weights are selected by minimizing a k-class generalized information criterion (k-GIC), which is an estimate of the average squared error from the model average fit. This model selection procedure is shown to be asymptotically optimal in the sense of obtaining the lowest possible average squared error. Monte Carlo simulations illustrate that the suggested method has comparable efficiency to some alternative model selection techniques.