Approximate tolerance intervals for nonparametric regression models

Yafan Guo, Derek S. Young

Research output: Contribution to journalArticlepeer-review


Tolerance intervals in regression allow the user to quantify, with a specified degree of confidence, bounds for a specified proportion of the sampled population when conditioned on a set of covariate values. While methods are available for tolerance intervals in fully-parametric regression settings, the construction of tolerance intervals for nonparametric regression models has been treated in a limited capacity. This paper fills this gap and develops likelihood-based approaches for the construction of pointwise one-sided and two-sided tolerance intervals for nonparametric regression models. A numerical approach is also presented for constructing simultaneous tolerance intervals. An appealing facet of this work is that the resulting methodology is consistent with what is done for fully-parametric regression tolerance intervals. Extensive coverage studies are presented, which demonstrate very good performance of the proposed methods. The proposed tolerance intervals are calculated and interpreted for analyses involving a fertility dataset and a triceps measurement dataset.

Original languageEnglish
Pages (from-to)212-239
Number of pages28
JournalJournal of Nonparametric Statistics
Issue number1
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2023 American Statistical Association and Taylor & Francis.


  • Bootstrap
  • boundary effects
  • coverage probabilities
  • k-factor
  • smoothing spline

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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