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On Optimal Point and Block Prediction in Log‐Gaussian Random Fields

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  • VICTOR DE OLIVEIRA

Abstract

. This work discusses the problems of point and block prediction in log‐Gaussian random fields with unknown mean. New point and block predictors are derived that are optimal in mean squared error sense within certain families of predictors that contain the corresponding lognormal kriging point and block predictors, as well as a block predictor originally motivated under the assumption of ‘preservation of lognormality’, and hence improve upon them. A comparison between the optimal, lognormal kriging and best linear unbiased predictors is provided, as well as between the two new block predictors. Somewhat surprisingly, it is shown that the corresponding optimal and lognormal kriging predictors are almost identical under most scenarios. It is also shown that one of the new block predictors is uniformly better than the other.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:33:y:2006:i:3:p:523-540
    DOI: 10.1111/j.1467-9469.2006.00494.x
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    Cited by:

    1. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Carlo Gaetan, 2020. "On modeling positive continuous data with spatiotemporal dependence," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
    2. Toshihiro Hirano & Yoshihiro Yajima, 2013. "Covariance tapering for prediction of large spatial data sets in transformed random fields," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 913-939, October.
    3. 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.
    4. Ganggang Xu & Marc G. Genton, 2017. "Tukey -and- Random Fields," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1236-1249, July.
    5. 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.
    6. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Reinaldo B. Arellano‐Valle & Víctor Morales‐Oñate, 2021. "Non‐Gaussian geostatistical modeling using (skew) t processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 212-245, March.

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