Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 210510, 10 pages
http://dx.doi.org/10.1155/2013/210510
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.

Linked References

  1. Z. Griliches and V. Ringstad, “Errors-in-the-variables bias in nonlinear contexts,” Econometrica, vol. 38, no. 2, pp. 368–370, 1970. View at Google Scholar
  2. W. A. Fuller, Measurement Error Models, John Wiley & Sons, New York, NY, USA, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. T. Erickson and T. M. Whited, “Two-step GMM estimation of the errors-in-variables model using high-order moments,” Econometric Theory, vol. 18, no. 3, pp. 776–799, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. P. J. Cornbleet and N. Gochman, “Incorrect least-squares regression coefficients,” Clinical Chemistry, vol. 25, no. 3, pp. 432–438, 1979. View at Google Scholar
  5. J. W. Gillard, “An historical overview of linear regression with errors in both variables,” Tech. Rep., Cardiff University School of Mathematics, Cardiff, UK, 2006. View at Google Scholar
  6. L. El Ghaoui and H. Lebret, “Robust solutions to least-squares problems with uncertain data,” SIAM Journal on Matrix Analysis and Applications, vol. 18, no. 4, pp. 1035–1064, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. P. K. Shivaswamy, C. Bhattacharyya, and A. J. Smola, “Second order cone programming approaches for handling missing and uncertain data,” Journal of Machine Learning Research, vol. 7, pp. 1283–1314, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. Ben-Tal, L. El Ghaoui, and A. Nemirovski, Robust Optimization, Princeton University Press, Princeton, NJ, USA, 2009. View at MathSciNet
  9. T. B. Trafalis and R. C. Gilbert, “Robust classification and regression using support vector machines,” European Journal of Operational Research, vol. 173, no. 3, pp. 893–909, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Xu, C. Caramanis, and S. Mannor, “Robustness and regularization of support vector machines,” Journal of Machine Learning Research, vol. 10, pp. 1485–1510, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. B. Trafalis and R. C. Gilbert, “Robust support vector machines for classification and computational issues,” Optimization Methods & Software, vol. 22, no. 1, pp. 187–198, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. P. J. Huber, Robust Statistics, John Wiley & Sons, New York, NY, USA, 1981. View at MathSciNet
  13. J. L. Wu and P. C. Chang, “A trend-based segmentation method and the support vector regression for financial time series forecasting,” Mathematical Problems in Engineering, vol. 2012, Article ID 615152, 20 pages, 2012. View at Publisher · View at Google Scholar
  14. D. X. She and X. H. Yang, “A new adaptive local linear prediction method and its application in hydrological time Series,” Mathematical Problems in Engineering, vol. 2010, Article ID 205438, 15 pages, 2010. View at Publisher · View at Google Scholar
  15. Z. Liu, “Chaotic time series analysis,” Mathematical Problems in Engineering, vol. 2010, Article ID 720190, 31 pages, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. M. Li, “Fractal time series: a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. T. Farooq, A. Guergachi, and S. Krishnan, “Knowledge-based green’s kernel for support vector regression,” Mathematical Problems in Engineering, vol. 2010, Article ID 378652, 16 pages, 2010. View at Publisher · View at Google Scholar
  18. I. Pólik and T. Terlaky, “A survey of the S-lemma,” SIAM Review, vol. 49, no. 3, pp. 371–418, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. K. C. Toh, R. H. Tütünü, and M. J. Todd, “On the implementation and usage of SDPT3Ca Matlab software package for semidefinitequadratic-linear programming,” version 4. 0, 2006, http://ecommons.library.cornell.edu/handle/1813/15133.
  20. J. Kraft and A. Kraft, “On the relationship between energy and GNP,” Journal of Energy and Development, vol. 3, no. 2, pp. 401–403, 1978. View at Google Scholar
  21. O. Ilhan, “A literature survey on energy growth nexus,” Energy Policy, vol. 38, pp. 340–349, 2010. View at Google Scholar
  22. N. Bowden and J. E. Payne, “The causal relationship between US energy consumption and real output: a disaggregated analysis,” Journal of Policy Modeling, vol. 31, no. 2, pp. 180–188, 2009. View at Google Scholar
  23. U. Soytas and R. Sari, “Energy consumption, economic growth, and carbon emissions: challenges faced by an EU candidate member,” Ecological Economics, vol. 68, no. 6, pp. 1667–1675, 2009. View at Google Scholar
  24. B. Cheng, “An investigation of cointegration and causality between energy consumption and economic growth,” Journal of Energy Development, vol. 21, no. 1, pp. 73–84, 1995. View at Google Scholar
  25. D. I. Stern, “Energy and economic growth in the USA: a multivariate approach,” Energy Economics, vol. 15, no. 2, pp. 137–150, 1993. View at Google Scholar
  26. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, UK, 2004. View at MathSciNet