Are Kriging's residuals (i.e. Z-Zhat) spatially independent?

by A. Tavassoli   Last Updated January 14, 2018 07:19 AM

Suppose data {Z(s_i ):i=1, ..., n} are observed at spatial locations {s_i :i=1, ..., n}. To carry out the spatial prediction (predict un unknown Z(s_0) at a known location s_0) we can use a method like ordinary Kriging.
I've used cross-validation for Kriging to create residuals to compare actual versus model’s predicted values. I know that for these residuals, RMSE (root mean square error) should be as small as possible. But my question is that is there any spatial dependence in these residuals?
Should Kriging's (or any other spatial prediction method's) residuals be independent? If the answer is YES, can I use this to compare two different spatial prediction methods? (I mean, the more the method remove the spatial dependency in residuals, the better it is).

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