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Adaptive Huber Regression

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  • Qiang Sun
  • Wen-Xin Zhou
  • Jianqing Fan

Abstract

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust estimation and inference. The key observation is that the robustification parameter should adapt to the sample size, dimension and moments for optimal tradeoff between bias and robustness. Our theoretical framework deals with heavy-tailed distributions with bounded (1+δ) th moment for any δ>0 . We establish a sharp phase transition for robust estimation of regression parameters in both low and high dimensions: when δ≥1 , the estimator admits a sub-Gaussian-type deviation bound without sub-Gaussian assumptions on the data, while only a slower rate is available in the regime 0

Suggested Citation

  • Qiang Sun & Wen-Xin Zhou & Jianqing Fan, 2020. "Adaptive Huber Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 254-265, January.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:529:p:254-265
    DOI: 10.1080/01621459.2018.1543124
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    Cited by:

    1. Xing, Li-Min & Zhang, Yue-Jun, 2022. "Forecasting crude oil prices with shrinkage methods: Can nonconvex penalty and Huber loss help?," Energy Economics, Elsevier, vol. 110(C).
    2. Xiaowei Yang & Xinqiao Liu & Haoyu Wei, 2022. "Concentration inequalities of MLE and robust MLE," Papers 2210.09398, arXiv.org, revised Dec 2022.
    3. Han, Dongxiao & Huang, Jian & Lin, Yuanyuan & Shen, Guohao, 2022. "Robust post-selection inference of high-dimensional mean regression with heavy-tailed asymmetric or heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 230(2), pages 416-431.
    4. Yang, Shuquan & Ling, Nengxiang, 2023. "Robust projected principal component analysis for large-dimensional semiparametric factor modeling," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    5. Luo, Jiyu & Sun, Qiang & Zhou, Wen-Xin, 2022. "Distributed adaptive Huber regression," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    6. Peter Bossaerts & Shijie Huang & Nitin Yadav, 2020. "Exploiting Distributional Temporal Difference Learning to Deal with Tail Risk," Risks, MDPI, vol. 8(4), pages 1-20, October.
    7. Donggyu Kim & Minseok Shin, 2023. "Volatility models for stylized facts of high‐frequency financial data," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(3), pages 262-279, May.
    8. Joaquim Fernando Pinto da Costa & Manuel Cabral, 2022. "Statistical Methods with Applications in Data Mining: A Review of the Most Recent Works," Mathematics, MDPI, vol. 10(6), pages 1-22, March.
    9. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    10. Elvezio Ronchetti, 2021. "The main contributions of robust statistics to statistical science and a new challenge," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 127-135, August.
    11. Xiao, Xuan & Xu, Xingbai & Zhong, Wei, 2023. "Huber estimation for the network autoregressive model," Statistics & Probability Letters, Elsevier, vol. 203(C).
    12. Yuyang Liu & Pengfei Pi & Shan Luo, 2023. "A semi-parametric approach to feature selection in high-dimensional linear regression models," Computational Statistics, Springer, vol. 38(2), pages 979-1000, June.
    13. Pan Shang & Lingchen Kong, 2021. "Regularization Parameter Selection for the Low Rank Matrix Recovery," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 772-792, June.
    14. Li, Kangqiang & Tang, Songqiao & Zhang, Lixin, 2022. "Robust parameter estimation of regression models under weakened moment assumptions," Statistics & Probability Letters, Elsevier, vol. 191(C).
    15. Chen, Huangyue & Kong, Lingchen & Shang, Pan & Pan, Shanshan, 2020. "Safe feature screening rules for the regularized Huber regression," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    16. Yijun Zuo, 2023. "Non-asymptotic analysis and inference for an outlyingness induced winsorized mean," Statistical Papers, Springer, vol. 64(5), pages 1465-1481, October.
    17. Qian Zhang & Xinyuan Zhao & Chao Ding, 2021. "Matrix optimization based Euclidean embedding with outliers," Computational Optimization and Applications, Springer, vol. 79(2), pages 235-271, June.
    18. Liang, Wanfeng & Wu, Yue & Ma, Xiaoyan, 2022. "Robust sparse precision matrix estimation for high-dimensional compositional data," Statistics & Probability Letters, Elsevier, vol. 184(C).
    19. Haoyu Wei & Hengrui Cai & Chengchun Shi & Rui Song, 2024. "On Efficient Inference of Causal Effects with Multiple Mediators," Papers 2401.05517, arXiv.org.
    20. Neil Shephard, 2020. "An estimator for predictive regression: reliable inference for financial economics," Papers 2008.06130, arXiv.org.
    21. Wang, Yibo & Karunamuni, Rohana J., 2022. "High-dimensional robust regression with Lq-loss functions," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    22. Donggyu Kim & Minseog Oh, 2023. "Dynamic Realized Minimum Variance Portfolio Models," Papers 2310.13511, arXiv.org.

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