Methods for estimating the semivariogram

Søren Nymand Lophaven, Niels Jacob Carstensen, Helle Rootzen

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    Modelling spatial variability, typically in terms of the semivariogram, is of great interest when the objective is to compute spatial predictions of parameters measured in space. Such parameters could be rainfall, temperature or concentrations of polluting agents in aquatic environments. In the existing literature various methods for modelling the semivariogram have been proposed, while only a few studies have been made on comparing different approaches. In this paper we compare eight approaches for modelling the semivariogram, i.e. six approaches based on least squares estimation of an experimental semivariogram, as well as maximum likelihood and restricted maximum likelihood estimation. The comparison is made by simulating spatial data with a known covariance structure, and comparing the "true" parameters with those computed. The comparison showed that maximum likelihood and restricted maximum likelihood performed better than the least squares approaches. We also applied maximum likelihood and least squares estimation to a real dataset, containing measurements of salinity at 71 sampling stations in the Kattegat basin. This showed that the calculation of spatial predictions is insensitive to the choice of estimation method, but also that the uncertainties of predictions were reduced when applying maximum likelihood.
    Original languageEnglish
    Title of host publicationSymposium i Anvendt Statistik
    PublisherInstitut for Informationsbehandling, Handelshøjskolen i Århus
    Publication date2002
    Publication statusPublished - 2002

    Cite this

    Lophaven, S. N., Carstensen, N. J., & Rootzen, H. (2002). Methods for estimating the semivariogram. In Symposium i Anvendt Statistik (pp. 128-144). Institut for Informationsbehandling, Handelshøjskolen i Århus.