ABSTRACT
Yakowitz and Szidarovszky (1985) posed what appeared to be a fundamental challenge to the use of kriging for spatial interpolation. Specifically, they noted that it is not generally possible to estimate consistently the variogram of a spatial process based on observations in a bounded domain and, hence, it was not clear that one could obtain good kriging predictors and good assessments of kriging variance based on estimated variograms even if one had a very large number of observations in some bounded domain of interest. It is still not possible to give a definitive response to this challenge, but there is now at least some good reason to believe that the objection raised by Yakowitz and Szidarovszky does not expose a fundamental flaw in the use of kriging for spatial interpolation. However, it is still very much the case that what might be considered very basic results in the large sample properties of kriging are unproven and, furthermore, the prospects of rigorous proofs appearing in the foreseeable future are not great.
