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Prediction intervals for integrals of Gaussian random fields

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  • De Oliveira, Victor
  • Kone, Bazoumana

Abstract

Methodology is proposed for the construction of prediction intervals for integrals of Gaussian random fields over bounded regions (called block averages in the geostatistical literature) based on observations at a finite set of sampling locations. Two bootstrap calibration algorithms are proposed, termed indirect and direct, aimed at improving upon plug-in prediction intervals in terms of coverage probability. A simulation study is carried out that illustrates the effectiveness of both procedures, and these procedures are applied to estimate block averages of chromium traces in a potentially contaminated region in Switzerland.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:37-51
    DOI: 10.1016/j.csda.2014.09.013
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    References listed on IDEAS

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    1. Masao Ueki & Kaoru Fueda, 2007. "Adjusting estimative prediction limits," Biometrika, Biometrika Trust, vol. 94(2), pages 509-511.
    2. 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.
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    4. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    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. Victor De Oliveira, 2006. "On Optimal Point and Block Prediction in Log‐Gaussian Random Fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 523-540, September.
    7. 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.
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    Cited by:

    1. Jun Yuan & Haowei Wang & Szu Hui Ng & Victor Nian, 2020. "Ship Emission Mitigation Strategies Choice Under Uncertainty," Energies, MDPI, vol. 13(9), pages 1-20, May.

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