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- W169069583 abstract "Many applications of kriging demand the introduction of a trend or external drift. We can use universal kriging, when we know the variogram of the process. But there are no straight forward methods known to estimate the variogram unbiasedly or consistently in the presence of a trend with unknown parameters. Thus the class of trend surfaces used is often restricted to polynomial trends leading to the application of intrinsic random functions and generalised covariograms. From the theory of intrinsic random functions IRFk we know that it is impossible to estimate the variogram unbiasedly in presence of a polynomial trend. It is shown that this problem comes up only with polynomial and harmonic trend surfaces. Thus polynomial trends are not the best but the worst case to consider. A method based on the statistical technique of identifiable contrasts for fitting the non–stationary variogram models is proposed and applications are presented in example situations. It works unbiasedly and consistently in the presence of internal and external drift and thus overcomes the crucial problem that the variogram could not be estimated unbiasedly in universal Kriging situations. It is shown that the theory of ∗Mathematics and Computer Sciences in Geology, Freiberg University of Mining and Technology, FRG †Friedrich–Alexander–Universitat, Institut fur Geographie, Kochstr. 4/4, 91054 Erlangen, Germany, e-mail: ali@proforma.de" @default.
- W169069583 created "2016-06-24" @default.
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- W169069583 date "2001-01-01" @default.
- W169069583 modified "2023-09-27" @default.
- W169069583 title "Why Universal Kriging is better than IRFk-Kriging: Estimation of Variograms in the Presence of Trend" @default.
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