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Distribution-free prediction bands for non-parametric regression

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  • Jing Lei
  • Larry Wasserman

Abstract

type="main" xml:id="rssb12021-abs-0001"> We study distribution-free, non-parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the idea of ‘conformal prediction’ with non-parametric conditional density estimation. The proposed estimator, called COPS (conformal optimized prediction set), always has a finite sample guarantee. Under regularity conditions the estimator converges to an oracle band at a minimax optimal rate. A fast approximation algorithm and a data-driven method for selecting the bandwidth are developed. The method is illustrated in simulated and real data examples.

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  • 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.
    • Handle: RePEc:bla:jorssb:v:76:y:2014:i:1:p:71-96
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    File URL: http://hdl.handle.net/10.1111/rssb.2013.76.issue-1
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    Citations

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    Cited by:

    1. Victor Chernozhukov & Kaspar Wüthrich & Yinchu Zhu, 2018. "Exact and robust conformal inference methods for predictive machine learning with dependent data," CeMMAP working papers CWP16/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Xie, Haihan & Kong, Linglong, 2023. "Gaussian copula function-on-scalar regression in reproducing kernel Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    3. Jean Feng & Arjun Sondhi & Jessica Perry & Noah Simon, 2023. "Selective prediction‐set models with coverage rate guarantees," Biometrics, The International Biometric Society, vol. 79(2), pages 811-825, June.
    4. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2019. "Distributional conformal prediction," Papers 1909.07889, arXiv.org, revised Aug 2021.
    5. Algo Carè & Simone Garatti & Marco C. Campi, 2017. "A coverage theory for least squares," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1367-1389, November.
    6. Zhang, Yingying & Shi, Chengchun & Luo, Shikai, 2023. "Conformal off-policy prediction," LSE Research Online Documents on Economics 118250, London School of Economics and Political Science, LSE Library.
    7. Hu, Jianming & Luo, Qingxi & Tang, Jingwei & Heng, Jiani & Deng, Yuwen, 2022. "Conformalized temporal convolutional quantile regression networks for wind power interval forecasting," Energy, Elsevier, vol. 248(C).
    8. David J. Olive, 2018. "Applications of hyperellipsoidal prediction regions," Statistical Papers, Springer, vol. 59(3), pages 913-931, September.
    9. Leying Guan, 2023. "Localized conformal prediction: a generalized inference framework for conformal prediction," Biometrika, Biometrika Trust, vol. 110(1), pages 33-50.
    10. João A. Bastos, 2023. "Conformal prediction of option prices," Working Papers REM 2023/0304, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

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