Abstract
It is common in geostatistics to use the variogram to describe the spatial dependence structure and to use kriging as the spatial prediction methodology. Both methods are sensitive to outlying observations and are strongly influenced by the marginal distribution of the underlying random field. Hence, they lead to unreliable results when applied to extreme value or multimodal data. As an alternative to traditional spatial modeling and interpolation we consider the use of copula functions. This paper extends existing copula-based geostatistical models. We show how location dependent covariates e.g. a spatial trend can be accounted for in spatial copula models. Furthermore, we introduce geostatistical copula-based models that are able to deal with random fields having discrete marginal distributions. We propose three different copula-based spatial interpolation methods. By exploiting the relationship between bivariate copulas and indicator covariances, we present indicator kriging and disjunctive kriging. As a second method we present simple kriging of the rank-transformed data. The third method is a plug-in prediction and generalizes the frequently applied trans-Gaussian kriging. Finally, we report on the results obtained for the so-called Helicopter data set which contains extreme radioactivity measurements.
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Acknowledgements
Copula-based spatial modeling and interpolation for continuous marginals is implemented in the \(\tt{R}\) statistical software as part of the \(\tt{intamap\,R}\)-library which is freely available from https://sourceforge.net/projects/intamap. IDW, Automap, PSGP and TGK are also implemented in this library. This work was partially funded by the European Commission, under the Sixth Framework Programme, by the Contract N. 033811 with DG INFSO, Action Line IST- 2005-2.5.12 ICT for Environmental Risk Management. The views expressed herein are those of the authors and are not necessarily those of the European Commission.
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Kazianka, H., Pilz, J. Copula-based geostatistical modeling of continuous and discrete data including covariates. Stoch Environ Res Risk Assess 24, 661–673 (2010). https://doi.org/10.1007/s00477-009-0353-8
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DOI: https://doi.org/10.1007/s00477-009-0353-8