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Mathematical Problems in Engineering
Volume 2013, Article ID 210510, 10 pages
Research Article

Robust Quadratic Regression and Its Application to Energy-Growth Consumption Problem

1College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130061, China
2Department of Automation, TNList, Tsinghua University, Beijing 100084, China
3Development and Research Center of China Geological Survey, Beijing 100037, China
4School of Earth Sciences and Resources, China University of Geosciences, Beijing 100083, China

Received 1 May 2013; Accepted 8 August 2013

Academic Editor: Yudong Zhang

Copyright © 2013 Yongzhi Wang et al. 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.


We propose a robust quadratic regression model to handle the statistics inaccuracy. Unlike the traditional robust statistic approaches that mainly focus on eliminating the effect of outliers, the proposed model employs the recently developed robust optimization methodology and tries to minimize the worst-case residual errors. First, we give a solvable equivalent semidefinite programming for the robust least square model with ball uncertainty set. Then the result is generalized to robust models under - and -norm critera with general ellipsoid uncertainty sets. In addition, we establish a robust regression model for per capital GDP and energy consumption in the energy-growth problem under the conservation hypothesis. Finally, numerical experiments are carried out to verify the effectiveness of the proposed models and demonstrate the effect of the uncertainty perturbation on the robust models.