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Journal of Probability and Statistics
Volume 2017, Article ID 2170816, 8 pages
https://doi.org/10.1155/2017/2170816
Research Article

Robust Group Identification and Variable Selection in Regression

Department of Statistics, College of Administration and Economics, University of Al-Qadisiyah, Al Diwaniyah, Iraq

Correspondence should be addressed to Ali Alkenani; qi.ude.uq@inanekla.ila

Received 16 September 2017; Accepted 3 December 2017; Published 20 December 2017

Academic Editor: Aera Thavaneswaran

Copyright © 2017 Ali Alkenani and Tahir R. Dikheel. 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. L. Breiman, “Heuristics of instability and stabilization in model selection,” The Annals of Statistics, vol. 24, no. 6, pp. 2350–2383, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  2. R. Tibshirani, “Regression shrinkage and selection via the lasso: A retrospective,” Journal of the Royal Statistical Society: Series B (Methodological), vol. 73, no. 3, pp. 273–282, 1996. View at Publisher · View at Google Scholar · View at Scopus
  3. J. Fan and R. Li, “Variable selection via nonconcave penalized likelihood and its oracle properties,” Journal of the American Statistical Association, vol. 96, no. 456, pp. 1348–1360, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” Journal of the Royal Statistical Society B: Statistical Methodology, vol. 67, no. 2, pp. 301–320, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. R. Tibshirani, M. Saunders, S. Rosset, J. Zhu, and K. Knight, “Sparsity and smoothness via the fused lasso,” Journal of the Royal Statistical Society B: Statistical Methodology, vol. 67, no. 1, pp. 91–108, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. H. Zou, “The adaptive lasso and its oracle properties,” Journal of the American Statistical Association, vol. 101, no. 476, pp. 1418–1429, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. M. Yuan and Y. Lin, “Model selection and estimation in regression with grouped variables,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 68, no. 1, pp. 49–67, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  8. H. D. Bondell and B. J. Reich, “Simultaneous regression shrinkage, variable selection, and supervised clustering of predictors with OSCAR,” Biometrics, vol. 64, no. 1, pp. 115–123, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. H. Zou and H. H. Zhang, “On the adaptive elastic-net with a diverging number of parameters,” The Annals of Statistics, vol. 37, no. 4, pp. 1733–1751, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. C.-H. Zhang, “Nearly unbiased variable selection under minimax concave penalty,” The Annals of Statistics, vol. 38, no. 2, pp. 894–942, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. D. B. Sharma, H. D. Bondell, and H. H. Zhang, “Consistent group identification and variable selection in regression with correlated predictors,” Journal of Computational and Graphical Statistics, vol. 22, no. 2, pp. 319–340, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. V. c. Yohai, “High breakdown-point and high efficiency robust estimates for regression,” The Annals of Statistics, vol. 15, no. 2, pp. 642–656, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  13. D. J. Olive and D. M. Hawkins, “Robust multivariate location and dispersion,” http://lagrange.math.siu.edu/Olive/pphbmld.pdf, 2010.
  14. R. Wilcox, Introduction to robust estimation and hypothesis testing, Statistical Modeling and Decision Science, Academic press, 2005. View at MathSciNet
  15. A. Alkenani and K. Yu, “A comparative study for robust canonical correlation methods,” Journal of Statistical Computation and Simulation, vol. 83, no. 4, pp. 690–720, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. W. D. Mangold, L. Bean, and D. Adams, “The Impact of Intercollegiate Athletics on Graduation Rates among Major NCAA Division I Universities: Implications for College Persistence Theory and Practice,” Journal of Higher Education, vol. 74, no. 5, pp. 540–563, 2003. View at Google Scholar · View at Scopus
  17. G. C. McDonald and R. C. Schwing, “Instabilities of regression estimates relating air pollution to mortality,” Technometrics, vol. 15, no. 3, pp. 463–481, 1973. View at Publisher · View at Google Scholar · View at Scopus