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I have a data set with only 47 soundings, so a small amount of data available. With this information I am trying to produce a raster surface through interpolation. Unfortunately, a data analysis showed that my data is not autocorrelated. So I chose a multivariate approach with the Geostatistical Analyst: Co-Kriging.

Now I am wondering if it is necessary to create a subset before doing the interpolation, because as far as I understand, the crossvalidation which can be done with the Geostatistical Analyst applies the leave-one-out technique. This means I can use the whole data set and still validate the results appropriately, right?

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This question has a general R coding framework for crossvalidation here. A jackknife would just be this approach with an n=1 and enough replicates to ensure that an error distribution is correctly represented.

Cokriging assumes the "coregionalized variable theory" as a rigid assumption, which is rarely met and most certainly violated with your data. This is not a supported approach just because your data are not autocorrelated and, in this case, is actually quite incorrect. Kriging assumes spatial structure in that the variance changes with distance and can be modeled as such via the semivariogram.

Alternately, you could apply an approach that does not assume spatial structure such as spline, IDW or polynomial regression. In the case of spline and polynomial regression, covariates can be included (but, not in ArcGIS). However, keep in mind that the resulting spatial pattern will be an artifact of the interpolator/model and not of any inherent spatial structure.

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