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Parametric variogram matrices incorporating both bounded and unbounded functions

Abstract

We construct a flexible class of parametric models for both traditional and pseudo variogram matrix (valued functions), where the off-diagonal elements are the traditional cross variograms and pseudo cross variograms, respectively, and the diagonal elements are the direct variograms, based on the method of latent dimensions and the linear model of coregionalization. The entries in the parametric variogram matrix allow for a smooth transition between boundedness and unboundedness by changing the values of parameters, and thus between joint second-order and intrinsically stationary vector random fields, or between multivariate geometric Gaussian processes and multivariate Brown–Resnick processes in spatial extreme analysis.

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Acknowledgements

The authors are grateful to Martin Schlather for providing the R code used in Schlather and Moreva (2017), based on which the visuanimations of direct and cross variograms in Movies 1 and 2 in the electronic supplementary material were produced. This research was supported by King Abdullah University of Science and Technology (KAUST).

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Correspondence to Wanfang Chen.

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Chen, W., Genton, M.G. Parametric variogram matrices incorporating both bounded and unbounded functions. Stoch Environ Res Risk Assess 33, 1669–1679 (2019). https://doi.org/10.1007/s00477-019-01710-1

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Keywords

  • Bounded and unbounded variogram
  • Cross variogram
  • Intrinsic stationarity
  • Second-order stationarity
  • Variogram matrix