Dear Mr. Milikan,

Variograms without sill, e.g. the linear variogram are typically related to 
intrinsic random fields, which have no second order stationarity and thus 
constant variance or covariance which can be defined for whole R^2.

To understand such fields Z(x) with variogramm gamma(h) it might be most 
simple think of K(x)= Z(x)-Z(0), with 0 representing some arbitrary but fixed 
origin of the field.  In this case K(x) has the covariance:

cov(K(x),K(y))= gamma(x)+gamma(y)-2gamma(x-y)

which for example gives:

var(K(0))=cov(K(0),K(0))= gamma(x)+gamma(y)-2gamma(x-y)=4gamma(0)=0

and var(K(h))=gamma(h)+gamma(h)-2gamma(0)=2gamma(h)

which is different for all different h. 

The interpretation of this is, that there is no common mean around which very 
locations at very distant points vary, such that it makes no sense to define 
a  variance Z(x) itself.

Even without beliving in such "strange" far range difference, this might be of 
practical importance, when the size of the observation region is small in 
relation to the total variance of the field such that it is impossible to 
estimate this variance or the global mean. 

Best regards,
Gerald v.d. Boogaart



Am Samstag, 26. August 2006 03:55 schrieb [EMAIL PROTECTED]:
> Hello,
>
>  I was wondering about some variogram models not having a
> sill.
> Does this mean that semi-variogram values can be greater
> than
> the population variance, in which case you would have
> negative
> covariances, or is the population variance the maximum these
> models, e.g. linear model, may reach.
> +
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-- 
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Prof. Dr. K. Gerald v.d. Boogaart
Professor als Juniorprofessor fuer Statistik
http://www.math-inf.uni-greifswald.de/statistik/  

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