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Confidence intervals for prediction intervals

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  • Rand Wilcox

Abstract

When working with a single random variable, the simplest and most obvious approach when estimating a 1 - γ prediction interval, is to estimate the γ/2 and 1 - γ/2 quantiles. The paper compares the small-sample properties of several methods aimed at estimating an interval that contains the 1 - γ prediction interval with probability 1 - α. In effect, the goal is to compute a 1 - α confidence interval for the true 1 - γ prediction interval. The only successful method when the sample size is small is based in part on an adaptive kernel estimate of the underlying density. Some simulation results are reported on how an extension to non-parametric regression performs, based on a so-called running interval smoother.

Suggested Citation

  • Rand Wilcox, 2006. "Confidence intervals for prediction intervals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(3), pages 317-326.
    • Handle: RePEc:taf:japsta:v:33:y:2006:i:3:p:317-326
    DOI: 10.1080/02664760500445962
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    References listed on IDEAS

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    1. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    2. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    3. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
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