IDEAS home Printed from
   My bibliography  Save this article

Distribution-Free Prediction Sets


  • Jing Lei
  • James Robins
  • Larry Wasserman


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

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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,
    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

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:108:y:2013:i:501:p:278-287. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.