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Robust MAVE through nonconvex penalized regression

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  • Zhang, Jing
  • Wang, Qin
  • Mays, D'Arcy

Abstract

High dimensionality has been a significant feature in modern statistical modeling. Sufficient dimension reduction (SDR) as an efficient tool aims at reducing the original high dimensional predictors without losing any regression information. Minimum average variance estimation (MAVE) is a popular approach in SDR among others. However, it is not robust to outliers in the response due to the use of least squares. A robust estimation through regularization with case-specific parameters is proposed to achieve robust estimation and outlier detection simultaneously. Under the nonconvex penalized regression framework, two efficient computational strategies are introduced. Simulation studies and a real data application show the efficacy of the proposed approach. Compared with existing methods, the proposed approach is less sensitive to the choice of initial estimators.

Suggested Citation

  • Zhang, Jing & Wang, Qin & Mays, D'Arcy, 2021. "Robust MAVE through nonconvex penalized regression," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:csdana:v:160:y:2021:i:c:s0167947321000815
    DOI: 10.1016/j.csda.2021.107247
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    References listed on IDEAS

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    1. 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.
    2. She, Yiyuan & Owen, Art B., 2011. "Outlier Detection Using Nonconvex Penalized Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 626-639.
    3. 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.
    4. Wu, Chaojiang & Yu, Yan, 2014. "Partially linear modeling of conditional quantiles using penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 170-187.
    5. Wang, Hansheng & Xia, Yingcun, 2008. "Sliced Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 811-821, June.
    6. 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.
    7. 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.
    8. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    9. Dong, Yuexiao & Yu, Zhou & Zhu, Liping, 2015. "Robust inverse regression for dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 71-81.
    10. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    11. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.
    12. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    13. Kong, Efang & Xia, Yingcun, 2012. "A Single-Index Quantile Regression Model And Its Estimation," Econometric Theory, Cambridge University Press, vol. 28(4), pages 730-768, August.
    14. Yao, Weixin & Wang, Qin, 2013. "Robust variable selection through MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 42-49.
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