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Improving coverage accuracy of nonparametric prediction intervals

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  • Peter Hall
  • Andrew Rieck

Abstract

Methods are suggested for improving the coverage accuracy of intervals for predicting future values of a random variable drawn from a sampled distribution. It is shown that properties of solutions to such problems may be quite unexpected. For example, the bootstrap and the jackknife perform very poorly when used to calibrate coverage, although the jackknife estimator of the true coverage is virtually unbiased. A version of the smoothed bootstrap can be employed for successful calibration, however. Interpolation among adjacent order statistics can also be an effective way of calibrating, although even there the results are unexpected. In particular, whereas the coverage error can be reduced from O(n‐1) to orders O(n‐2) and O(n‐3) (where n denotes the sample size) by interpolating among two and three order statistics respectively, the next two orders of reduction require interpolation among five and eight order statistics respectively.

Suggested Citation

  • Peter Hall & Andrew Rieck, 2001. "Improving coverage accuracy of nonparametric prediction intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 717-725.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:4:p:717-725
    DOI: 10.1111/1467-9868.00308
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    Cited by:

    1. Dag Kolsrud, 2015. "A Time‐Simultaneous Prediction Box for a Multivariate Time Series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(8), pages 675-693, December.
    2. Wang, Hsiuying, 2008. "Coverage probability of prediction intervals for discrete random variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 17-26, September.

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