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Title: Robust cross-variogram estimators and their distributions Authors:  Alfonso Garcia-Perez - UNED (Spain) [presenting]
Abstract: Let Z(s)=(Z_1(s),...,Z_p(s))^t be a multivariate spatial process that satisfies the intrinsic stationarity property. Assuming that we have a sample of Z(s) at n locations, we measure the statistical association between the random components of Z with the correlation coefficient and the spatial dependence with the variograms. To capture the association both within components of Z(s) and across s, we need the cross-variogram, defined for collocated data, i.e., assuming that each location has all variables Z_i measured, as 2\gamma_{ij}(h)=E[(Z_i(s+h)-Z_i(s))(Z_j(s+h)- Z_j(s))]. We define robust estimators of the cross-variogram and we obtain a saddlepoint approximation for their sample distributions, assuming a multivariate scale contaminated normal distribution as model.