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Robust variable selection through MAVE

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  • Yao, Weixin
  • Wang, Qin

Abstract

Dimension reduction and variable selection play important roles in high dimensional data analysis. The sparse MAVE, a model-free variable selection method, is a nice combination of shrinkage estimation, Lasso, and an effective dimension reduction method, MAVE (minimum average variance estimation). However, it is not robust to outliers in the dependent variable because of the use of least-squares criterion. A robust variable selection method based on sparse MAVE is developed, together with an efficient estimation algorithm to enhance its practical applicability. In addition, a robust cross-validation is also proposed to select the structural dimension. The effectiveness of the new approach is verified through simulation studies and a real data analysis.

Suggested Citation

  • Yao, Weixin & Wang, Qin, 2013. "Robust variable selection through MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 42-49.
    • Handle: RePEc:eee:csdana:v:63:y:2013:i:c:p:42-49
    DOI: 10.1016/j.csda.2013.01.021
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    References listed on IDEAS

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    1. Cizek, P. & Hardle, W., 2006. "Robust estimation of dimension reduction space," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 545-555, November.
    2. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    3. Zhu, Yu & Zeng, Peng, 2006. "Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1638-1651, December.
    4. Liqiang Ni & R. Dennis Cook & Chih-Ling Tsai, 2005. "A note on shrinkage sliced inverse regression," Biometrika, Biometrika Trust, vol. 92(1), pages 242-247, March.
    5. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    6. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    7. Howard D. Bondell & Lexin Li, 2009. "Shrinkage inverse regression estimation for model‐free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 287-299, January.
    8. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    9. Ye Z. & Weiss R.E., 2003. "Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 968-979, January.
    10. Lexin Li & R. Dennis Cook & Christopher J. Nachtsheim, 2005. "Model‐free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 285-299, April.
    11. Wang, Qin & Yin, Xiangrong, 2008. "A nonlinear multi-dimensional variable selection method for high dimensional data: Sparse MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4512-4520, May.
    12. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    13. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    Cited by:

    1. Zhang, Jing & Wang, Qin & Mays, D'Arcy, 2021. "Robust MAVE through nonconvex penalized regression," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    2. Dernoncourt, David & Hanczar, Blaise & Zucker, Jean-Daniel, 2014. "Analysis of feature selection stability on high dimension and small sample data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 681-693.
    3. Lv, Jing & Yang, Hu & Guo, Chaohui, 2015. "An efficient and robust variable selection method for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 74-88.
    4. Rekabdarkolaee, Hossein Moradi & Boone, Edward & Wang, Qin, 2017. "Robust estimation and variable selection in sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 146-157.

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