I'm hesitant to participate for fear of being jumped on, but
I think there is another aspect to the original question that
has not been addressed.
From a practical standpoint, we have complete discretion in choosing
a model. In theory, the properties of the sample do not inform the choice.
That being said, I wonder why one would choose a random model with no sill
(i.e., assume that the covariance function doesn't exist) rather than
a non-stationary model? If the covariance function exists, then C(0)
is your constant, and produces the odd result for a linear model that
the covariance between more distant locations becomes increasingly
negative. If the empirical semivariogram doesn't reach a sill near the
overall
variance of the sample=C(0), I would, consider choosing a different model
that used covariates to remove drift, or vary the sill in different
strata/regions if there is truly heteroscedascicity.
I think part of the difficulty in the semivariogram vs. covariance war
is that modeling is subjective, and the notion of covariance has become
more intuitive for statisticians, while the notion of semivariance has
become more intuitive for geologists.
Yetta
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