Dear Digby Millikan,

> , and was curious as to weather other
> values could be used or only the mean was appropriate.

We distinguish an empirical and a theoretical variogram:

The theoretical variogram is the expected value of the squared difference. The 
empirical variogram is the mean of the actually observed squared differences. 
In principle the correct value would be the value of the theoretical 
variogram. However the theoretical value is not observable and thus we take 
the best approximation we have, e.g. a value from a variogram model fitted to 
the means of the observed values. Other estimators, e.g. more robust ones,  
have been proposed e.g. by Cressie, but the use of the mean is still state of 
the art, when robustness is not important. 

When you are so interested in the basics of geostatistics it might be a good 
idea to work through one the books focusing more on the theory. I personally 
found the book of Cressie very helpfull in this direction, but also the books 
of Wackernagel and  Chiles/Delfiner might give a more complete view to the 
mathematical background.

Best regards,
Gerald  


Am Freitag, 15. September 2006 10:27 schrieb Digby Millikan:
> , and was curious as to weather other
> values could be used or only the mean was appropriate.

-- 
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Prof. Dr. K. Gerald v.d. Boogaart
Professor als Juniorprofessor fuer Statistik
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