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Distribution-Free Prediction Sets

Author

Listed:
  • Jing Lei
  • James Robins
  • Larry Wasserman

Abstract

This article introduces a new approach to prediction by bringing together two different nonparametric ideas: distribution-free inference and nonparametric smoothing. Specifically, we consider the problem of constructing nonparametric tolerance/prediction sets. We start from the general conformal prediction approach, and we use a kernel density estimator as a measure of agreement between a sample point and the underlying distribution. The resulting prediction set is shown to be closely related to plug-in density level sets with carefully chosen cutoff values. Under standard smoothness conditions, we get an asymptotic efficiency result that is near optimal for a wide range of function classes. But the coverage is guaranteed whether or not the smoothness conditions hold and regardless of the sample size. The performance of our method is investigated through simulation studies and illustrated in a real data example.

Suggested Citation

  • Jing Lei & James Robins & Larry Wasserman, 2013. "Distribution-Free Prediction Sets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 278-287, March.
  • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:501:p:278-287
    DOI: 10.1080/01621459.2012.751873
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    File URL: http://hdl.handle.net/10.1080/01621459.2012.751873
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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. Mammen, Enno & Martínez Miranda, María Dolores & Nielsen, Jens Perch, 2015. "In-sample forecasting applied to reserving and mesothelioma mortality," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 76-86.
    3. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2019. "Distributional conformal prediction," Papers 1909.07889, arXiv.org.
    4. repec:bla:jorssb:v:79:y:2017:i:5:p:1367-1389 is not listed on IDEAS
    5. Victor Chernozhukov & Kaspar Wüthrich & Yu Zhu, 2017. "An exact and robust conformal inference method for counterfactual and synthetic controls," CeMMAP working papers CWP62/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. repec:spr:stpapr:v:59:y:2018:i:3:d:10.1007_s00362-016-0796-1 is not listed on IDEAS

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