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The Bootstrap and Kriging Prediction Intervals

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  • Sara Sjöstedt‐de Luna
  • Alastair Young

Abstract

Kriging is a method for spatial prediction that, given observations of a spatial process, gives the optimal linear predictor of the process at a new specified point. The kriging predictor may be used to define a prediction interval for the value of interest. The coverage of the prediction interval will, however, equal the nominal desired coverage only if it is constructed using the correct underlying covariance structure of the process. If this is unknown, it must be estimated from the data. We study the effect on the coverage accuracy of the prediction interval of substituting the true covariance parameters by estimators, and the effect of bootstrap calibration of coverage properties of the resulting ‘plugin’ interval. We demonstrate that plugin and bootstrap calibrated intervals are asymptotically accurate in some generality and that bootstrap calibration appears to have a significant effect in improving the rate of convergence of coverage error.

Suggested Citation

  • Sara Sjöstedt‐de Luna & Alastair Young, 2003. "The Bootstrap and Kriging Prediction Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 175-192, March.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:1:p:175-192
    DOI: 10.1111/1467-9469.00325
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    Cited by:

    1. Paige, John & Fuglstad, Geir-Arne & Riebler, Andrea & Wakefield, Jon, 2022. "Bayesian multiresolution modeling of georeferenced data: An extension of ‘LatticeKrig’," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    2. Li, Mingyang & Wang, Zequn, 2019. "Surrogate model uncertainty quantification for reliability-based design optimization," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    3. De Oliveira, Victor & Kone, Bazoumana, 2015. "Prediction intervals for integrals of Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 37-51.
    4. D den Hertog & J P C Kleijnen & A Y D Siem, 2006. "The correct Kriging variance estimated by bootstrapping," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 400-409, April.
    5. De Oliveira, Victor & Rui, Changxiang, 2009. "On shortest prediction intervals in log-Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4345-4357, October.
    6. Federica Giummolè & Paolo Vidoni, 2010. "Improved prediction limits for a general class of Gaussian models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 483-493, November.
    7. Hartman, Linda & Hossjer, Ola, 2008. "Fast kriging of large data sets with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2331-2349, January.

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