Dear Pascal,

In agreement with Kevin, I find it possible but not common. In Table 3 of Li and Heap (2011) (Article A review of comparative studies of spatial interpolation met...

Be careful: the measure you used for assessing performance might has impact on your findings...

HTH,

Ákos

Pascal,

That may seem counterintuitive but it’s not surprising when you consider the consequences of fitting a model and then fitting a further model (through kriging) to the error structure. Kriging works well when it has a well defined smooth local structure to fit to. If the initial model fit through regression removes the local correlation structure then Kriging will not improve the fit.

Dear Pascal,

In agreement with Kevin, I find it possible but not common. In Table 3 of Li and Heap (2011) (Article A review of comparative studies of spatial interpolation met...

Be careful: the measure you used for assessing performance might has impact on your findings...

HTH,

Ákos

Inverse distance weighting interpolation is only a heuristic method, it is not based on any theory nor on any statistical assumptions. It depends only on the intuitive idea that values at two locations close together are more "similar" than the values at two locations far apart. But of course the term "similar" is not a quantitative measure. You can do the cross-validation computations (one data location at a time withhold the value when applying IWD to interpolate at the specified data location) You then have for each data location two values, the original data value and the cross validated value. In general these will not be the same. You can compute various statistics, e.g. mean difference, mean absolute difference, median difference, root mean square, etc but you have no theory to determine what these statistics mean or how to interpret them. Note that your results also depend on exactly how you do the IWD, e.g. what exponent you use on the inverse distance, the shape of the search neighborhood and the number of data locations in the search neighborhood. If you look at the numerical analysis literature you will find a number of papers about this.

In contrast ordinary kriging is based on several assumptions; the data is a non random sample from one realization of an intrinsic stationary random function, the variogram is modeled based on the data, the interpolator/estimator is a weighted linear combination of data, the weights are obtained as the solution of a linear system of equations. That system is obtained by minimizing the estimation variance and requiring the estimator to be unbiased.

Because the estimator is unbiased the expected value of the mean difference is theoretically zero. The expected value of the root mean square of the normalized differences is one. The differences need not be normally distributed but using the Tschebychev Inequality you get a bound on the proportion of mean differences exceeding various limits

See

1991, Myers,D.E., On Variogram Estimation in Proceedings of the First Inter. Conf. Stat. Comp., Cesme, Turkey, 30 Mar.-2 April 1987, Vol II, American Sciences Press, 261-281

Cross validation is useful for several purposes

1. To compare two different variogram models/variogram parameters (it won't tell you the "best"

2. The sensitivity of the ordinary kriging results to the search neighborhood parameters

Also see

1990, A.W. Warrick, R. Zhang, M.M. Moody and D.E. Myers, Kriging Versus Alternative Interpolators: Errors and Sensitivity to Model Inputs - in Field-Scale Water and Solute Flux in Soils (Monte Verita),(eds)Roth, Fl�hler, and Jury � Birkhauser Verlag Basel

Instead of combining ordinary kriging with regression you should use Universal kriging. Note that the statistical assumptions for regression are not the same as those for kriging, this discrepancy is even greater for the other methods you mention