I guess I forgot to send this to the list, so my apologies to Njeri for sending this twice...
For OK, the Lagrange multiplier is (1-sum of simple kriging weights) inv(sum(sum(inv(C))))) See Cressie, p. 123 for a start, but as I recall, Chiles and Delfiner have a nice section on this as well. This last term is 1 over the information matrix for estimating a mean. It gets large with strong correlation (we can't estimate the mean as precisely due to data redundancy) The first term is the difference between the simple kriging weights and 1 (i.e. how "strong" our constraint on summing to 1 is). The SK weights tend to sum closer to 1 if the prediction point is close to other data. So if we predict close to other data, the error in estimating the global mean matters less. If we are predicting far from the data, precise estimates of the global mean are important, if we are close to the data, not so important. Taken together, the lagrange multiplier helps to measure the portion of our prediction error that is due to estimating the mean in the first place. A good description of kriging as a regression and without using multipliers appeared some time ago (early-mid 90s?) in an article by Stein and Corsten in JASA. Hope this helps Cheers, Nicholas Nicholas N. Nagle, Assistant Professor University of Colorado Department of Geography UCB 260, Guggenheim 110 Boulder, CO 80309-0260 phone: 303-492-4794 Quoting Njeri Wabiri <[EMAIL PROTECTED]>: > Dear list > Just a newbabie question > What is the statistical interpretation of the Lagrange multiplier in > kriging. > At least I know if its positive we have a high kriging variance and vice > versa. > > Grateful for a response and a reference > > Njeri > > + > + To post a message to the list, send it to ai-geostats@jrc.it > + 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/ > + + To post a message to the list, send it to ai-geostats@jrc.it + 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/
