On the pseudo cross-variogram |
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Authors: | A. Papritz H. R. Künsch R. Webster |
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Affiliation: | 1. Institute of Terrestrial Ecology, ETH Zürich, Soil Physics, Grabenstrasse 3, 8952, Schlieren, Switzerland 2. Seminar for Statistics, ETH Zürich, Sonneggstrasse 33, 8092, Zürich, Switzerland
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Abstract: | 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. |
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