Dear Gregoire,
> > Still, part of the question remained unanswered. We all agree that in > .... > The real issue was however the fact that the investigated dataset was > not considered to present a pure nugget efffect! > .... > > What are thus the requirements for not observing this decrease and how > (linearly?) are both correlations (spatial correlation of observed > values versus the correlation between observations and residuals) > linked? > Lets tackle the problem with pure theory (for simplicity with a second order stationary field with simple kriging): Let us start from the simple equation : Z(x)= R(x)+K(x) Where Z(x) is the value of the field, K(x) is the kriging prediction and R(x) is the Residual. The kriging error is defined as var(R(x)) For the Simple Kriging predictor we have according to Gauss-Markov Theorem: cov(R(x),K(x))=0 And thus cov(Z(x),R(x))=cov(R(x)+K(x),R(x))=cov(R(x),R(x))+cov(K(x),R(x))= =cov(R(x),R(x))=var(R(x))=Kriging Error Thus the correlation is given by cor(Z(x),R(x))=var(R(x))/sqrt(var(R(x))var(Z(x))= sqrt(var(R(x))/sqrt(var(Z(x)))= = Kriging Standard deviation / Standard deviation of the Field Thus in simplified theory the correlation is given by the square root of the ratio of the kriging error devided by the sill: cor(Z(x),R(x))=sqrt( Kriging error / sill of variogramm) Does this formula explain your findings? The important parameter would thus not be directly the spatial correlation, but the kriging error resulting from it and the spatial arrangements of measurements. Best regards, Gerald -- ------------------------------------------------- Prof. Dr. K. Gerald v.d. Boogaart Professor als Juniorprofessor fuer Statistik http://www.stat.boogaart.de http://www.math-inf.uni-greifswald.de/statistik/ B�ro: Franz-Mehring-Str. 48, 1.Etage rechts e-mail: [EMAIL PROTECTED] phone: 00+49 (0)3834/86-4621 fax: 00+49 (0)3834/86-4615 (Institut) paper-mail: Ernst-Moritz-Arndt-Universitaet Greifswald Institut f�r Mathematik und Informatik Jahnstr. 15a 17487 Greifswald Germany -------------------------------------------------- + + To post a message to the list, send it to [email protected] + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
