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Conformal prediction for robust deep nonparametric regression

Author

Listed:
  • Jingsen Kong

    (Jinan University)

  • Yiming Liu

    (Jinan University)

  • Guangren Yang

    (Jinan University)

  • Wang Zhou

    (National University of Singapore)

Abstract

Conformal prediction is a general method used to convert a point predictor into a prediction band. The accuracy of this prediction band is heavily reliant on the base estimator. This paper is to investigate the use of conformal prediction by least absolute deviation-based deep nonparametric regression. We demonstrate the consistency of the robust deep regression estimator under mild conditions, leading to the proposed prediction band exhibiting finite-sample marginal validity and asymptotic conditional validity. Through extensive simulation studies and a real-data example, we illustrate the benefits of conformal prediction for robust deep regression.

Suggested Citation

  • Jingsen Kong & Yiming Liu & Guangren Yang & Wang Zhou, 2025. "Conformal prediction for robust deep nonparametric regression," Statistical Papers, Springer, vol. 66(1), pages 1-36, January.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01631-4
    DOI: 10.1007/s00362-024-01631-4
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    References listed on IDEAS

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    1. Wei Zhong & Chuang Wan & Wenyang Zhang, 2022. "Estimation and Inference for Multi-Kink Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1123-1139, June.
    2. Max H. Farrell & Tengyuan Liang & Sanjog Misra, 2021. "Deep Neural Networks for Estimation and Inference," Econometrica, Econometric Society, vol. 89(1), pages 181-213, January.
    3. Jing Lei & Larry Wasserman, 2014. "Distribution-free prediction bands for non-parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 71-96, January.
    4. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2019. "Distributional conformal prediction," Papers 1909.07889, arXiv.org, revised Aug 2021.
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