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Improved nonparametric tolerance intervals based on interpolated and extrapolated order statistics

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  • Derek S. Young
  • Thomas Mathew

Abstract

The standard approach to construct nonparametric tolerance intervals is to use the appropriate order statistics, provided a minimum sample size requirement is met. However, it is well-known that this traditional approach is conservative with respect to the nominal level. One way to improve the coverage probabilities is to use interpolation. However, the extension to the case of two-sided tolerance intervals, as well as for the case when the minimum sample size requirement is not met, have not been studied. In this paper, an approach using linear interpolation is proposed for improving coverage probabilities for the two-sided setting. In the case when the minimum sample size requirement is not met, coverage probabilities are shown to improve by using linear extrapolation. A discussion about the effect on coverage probabilities and expected lengths when transforming the data is also presented. The applicability of this approach is demonstrated using three real data sets.

Suggested Citation

  • Derek S. Young & Thomas Mathew, 2014. "Improved nonparametric tolerance intervals based on interpolated and extrapolated order statistics," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 415-432, September.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:415-432
    DOI: 10.1080/10485252.2014.906594
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    Cited by:

    1. Kedai Cheng & Derek S. Young, 2023. "An Approach for Specifying Trimming and Winsorization Cutoffs," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(2), pages 299-323, June.
    2. Jesse Frey & Yimin Zhang, 2017. "What Do Interpolated Nonparametric Confidence Intervals for Population Quantiles Guarantee?," The American Statistician, Taylor & Francis Journals, vol. 71(4), pages 305-309, October.
    3. Hund, Lauren & Schroeder, Benjamin & Rumsey, Kellin & Huerta, Gabriel, 2018. "Distinguishing between model- and data-driven inferences for high reliability statistical predictions," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 201-210.
    4. Kyung Serk Cho & Hon Keung Tony Ng, 2021. "Tolerance intervals in statistical software and robustness under model misspecification," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-49, December.

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