Dear Mr. Andrews, > Kriged estimate can not have always its own variance since kriged > estimate can not be always considered (thanks God !!!) as the central > value.
I only partially agree with your clearification: A variance is general concept for random variables. And random variables might or might not have variances. This is not a priviledge of central values. So under some assumptions (i.e. second order stationarity of the field) it is well true that kriging predictors have a variance even if this variance might be unknown and even when the kriging predictor is not intended to be a central value. The problem is more complicated: In classical unbiased estimation theory the variance of the estimator tells us something about its precision of the estimation by the equation: Var( Estimator ) = E[ ( Estimator - trueFixedValue )^2 ] however for unbiased predictors a similar equality does not hold : Var( Predictor(x) ) not= E[ ( Predictor(x) - trueRandomValue(x) )^2 ] However the right hand side of this equation is the relevant description of the precision of the prediciton and not the left hand side. And this right hand side becomes the the left hand side only in the special case of nonrandom values. And clearly E[ ( Predictor(x) - trueRandomValue(x) )^2 ] and Var( Predictor(x) ) depend on x which means that each predictor and each prediction error ( Predictor(x) - trueRandomValue(x) ) have their own variance. And nobody wants to claim something different!!! However things become more complicated just because the Var( Predictor(x) ) does not need to exist, and since is not identifiable even if exists if the mean of the field is unkown, und does definitly not exist for generalized (e.g. intrinsic) random fields. And this makes it so difficult to debate on that subject properly: The existence problem is quite unrelated to kriging and emerges from the mathematical model. However it implies that one can not just say: Yes, each kriging predictor has its own variance, but that variance is irrelevant for the description of the precession of the prediction. Best regards, Gerald v.d. Boogaart Am Donnerstag, 27. Juli 2006 10:05 schrieb tom andrews: > Dear Jan W Merks > > > ABSTRACT (as You wish): > Yes each distance-weighted average that is considered as the central > value has its own variance but no each distance-weighted average has to > have its own variance since no each distance-weighted average can be > considered as the central value. > > BODY: > If the distance-weighted average (mean) is taking into consideration as > the central value then the kriged estimate (mean) has its own variance > equal to the kriging variance multiplied by the sum of kriging weight > squares since in such case the kriging variance is the constant variance of > the process. Please, see http://arxiv.org/abs/cs.NA/0409033 for details. > > SUMMARY: > Kriged estimate can not have always its own variance since kriged > estimate can not be always considered (thanks God !!!) as the central > value. > > Best Regards > Tomasz Suslo > > > --------------------------------- > Talk is cheap. Use Yahoo! Messenger to make PC-to-Phone calls. Great rates > starting at 1¢/min. -- ------------------------------------------------- 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/
