On the pseudo cross-variogram

Normal cross-variograms cannot be estimated from data in the usual way when there are only a few points where both variables have been measured. But the experimental pseudo cross-variogram can be computed even where there are no matching sampling points, and this appears as its principal advantage. The pseudo cross-variogram may be unbounded, though for its existence the intrinsic hypothesis alone is not a sufficient stationarity condition. In addition the differences between the two random processes must be second order stationary. Modeling the function by linear coregionalization reflects the more restrictive stationarity condition: the pseudo cross-variogram can be unbounded only if the unbounded correlation structures are the same in all variograms. As an alternative to using the pseudo cross-variogram a new method is presented that allows estimating the normal cross variogram from data where only one variable has been measured at a point.