GENERALIZED CROSS-COVARIANCES AND THEIR ESTIMATION

Generalized cross-covariances describe the linear relationships betwee n spatial variables observed at different locations. They are invarian t 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, t hat is if the variograms are bounded, they correspond to the stationar y cross-covariances. Under some symmetry condition they are equal to m inus 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 obs erved at the same points. For fitting a linear coregionalization model we combine this new method with a standard algorithm which ensures po sitive definite coregionalization matrices. We study the behavior of t he method both by computing variances exactly and by simulating from v arious models.