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