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Robust high-dimensional regression for data with anomalous responses

Author

Listed:
  • Mingyang Ren

    (University of Chinese Academy of Sciences
    Chinese Academy of Sciences)

  • Sanguo Zhang

    (University of Chinese Academy of Sciences
    Chinese Academy of Sciences)

  • Qingzhao Zhang

    (Xiamen University)

Abstract

The accuracy of response variables is crucially important to train regression models. In some situations, including the high-dimensional case, response observations tend to be inaccurate, which would lead to biased estimators by directly fitting a conventional model. For analyzing data with anomalous responses in the high-dimensional case, in this work, we adopt γ-divergence to conduct variable selection and estimation methods. The proposed method possesses good robustness to anomalous responses, and the proportion of abnormal data does not need to be modeled. It is implemented by an efficient coordinate descent algorithm. In the setting where the dimensionality p can grow exponentially fast with the sample size n, we rigorously establish variable selection consistency and estimation bounds. Numerical simulations and an application on real data are presented to demonstrate the performance of the proposed method.

Suggested Citation

  • Mingyang Ren & Sanguo Zhang & Qingzhao Zhang, 2021. "Robust high-dimensional regression for data with anomalous responses," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 703-736, August.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:4:d:10.1007_s10463-020-00764-1
    DOI: 10.1007/s10463-020-00764-1
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    References listed on IDEAS

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    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273, December.
    2. 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.
    3. Hung Hung & Zhi†Yu Jou & Su†Yun Huang, 2018. "Robust mislabel logistic regression without modeling mislabel probabilities," Biometrics, The International Biometric Society, vol. 74(1), pages 145-154, March.
    4. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    5. 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.
    6. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
    7. Kenichi Hayashi, 2012. "A boosting method with asymmetric mislabeling probabilities which depend on covariates," Computational Statistics, Springer, vol. 27(2), pages 203-218, June.
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