Approximate tolerance intervals for nonparametric regression models

Abstract

AbstractTolerance 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.Keywords: Bootstrapboundary effectscoverage probabilitiesk-factorsmoothing splineAMS Subject Classifications: 62G0862G15 AcknowledgmentsWe would thank the University of Kentucky Center for Computational Sciences and Information Technology Services Research Computing for their support and use of the Lipscomb Compute Cluster and associated research computing resources. The authors are also thankful to the Associate Editor and two reviewers who provided numerous insightful comments that improved the overall quality of this work.Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementThe fertility data are available at the HFC's website bluehttps://www.fertilitydata.org/cgi-bin/data.php. The triceps data are available in the R package MultiKink (Wan and Zhong Citation2020), and can be accessed by typing data(triceps).