Mathematical Geology

, Volume 29, Issue 6, pp 779–799 | Cite as

Generalized cross-covariances and their estimation

  • H. R. Künsch
  • A. Papritz
  • F. Bassi


Generalized cross-covariances describe the linear relationships between spatial variables observed at different locations. They are invariant under translation of the locations for any intrinsic processes, they determine the cokriging predictors without additional assumptions and they are unique up to linear functions. If the model is stationary, that is if the variograms are bounded, they correspond to the stationary cross-covariances. Under some symmetry condition they are equal to minus the usual cross-variogram. We present a method to estimate these generalized cross-covariances from data observed at arbitrary sampling locations. In particular we do not require that all variables are observed at the same points. For fitting a linear coregionalization model we combine this new method with a standard algorithm which ensures positive definite coregionalization matrices. We study the behavior of the method both by computing variances exactly and by simulating from various models.

Key words

multivariate intrinsic processes cokriging cross-correlations variance of increments undersampling coregionalization 


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Copyright information

© International Association for Mathematical Geology 1997

Authors and Affiliations

  1. 1.ETH Zurich, Seminar for StatisticsZurichSwitzerland
  2. 2.Institute of Terrestrial EcologyETH Zurich, Soil PhysicsSchlierenSwitzerland

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