Variogram model selection via nonparametric derivative estimation

David J. Gorsich*, Marc G. Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

Before optimal linear prediction can be performed on spatial data sets, the variogram is usually estimated at various lags and a parametric model is fitted to those estimates. Apart from possible a priori knowledge about the process and the user's subjectivity, there is no standard methodology for choosing among valid variogram models like the spherical or the exponential ones. This paper discusses the nonparametric estimation of the variogram and its derivative, based on the spectral representation of positive definite functions. The use of the estimated derivative to help choose among valid parametric variogram models is presented. Once a model is selected, its parameters can be estimated-for example, by generalized least squares. A small simulation study is performed that demonstrates the usefulness of estimating the derivative to help model selection and illustrates the issue of aliasing. MATLAB software for nonparametric variogram derivative estimation is available at http://www-math.mit.edu/()gorsich/derivative.html. An application to the Walker Lake data set is also presented.

Original languageEnglish (US)
Pages (from-to)249-270
Number of pages22
JournalMathematical Geology
Volume32
Issue number3
DOIs
StatePublished - 2000
Externally publishedYes

Keywords

  • Aliasing
  • Derivative estimation
  • Generalized least squares
  • Model selection
  • Nonparametric
  • Variogram fitting

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Earth and Planetary Sciences (miscellaneous)

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