New Robust Cross-Variogram Estimators and Approximations of Their Distributions Based on Saddlepoint Techniques

Let Z(s)=(Z1(s),…,Zp(s))t be an isotropic second-order stationary multivariate spatial process. We measure the statistical association between p random components of Z with correlation coefficients and dependence variograms. If two are correlated, information provided by one them can improve other. To capture this association, both within Z(s) across s, we use a cross-variogram. Only robust cross-variogram estimators have been proposed in literature, Lark, their sample distributions were not obtained. In paper, propose new estimators, following location estimation method instead scale considered thus extending results obtained García-Pérez to case. also obtain accurate approximations for using saddlepoint techniques assuming multivariate-scale contaminated normal model. The question independence transformed variables avoid usual observations is linking it acceptance linear variograms cross-variograms.