Environmental Earth Sciences

, Volume 66, Issue 2, pp 615–624

An approach for valid covariance estimation via the Fourier series

  • Pilar García-Soidán
  • Raquel Menezes
  • Óscar Rubiños-López
Original Article

Abstract

The use of kriging for construction of prediction or risk maps requires estimating the dependence structure of the random process, which can be addressed through the approximation of the covariance function. The nonparametric estimators used for the latter aim are not necessarily valid to solve the kriging system, since the positive-definiteness condition of the covariance estimator typically fails. The usage of a parametric covariance instead may be attractive at first because of its simplicity, although it may be affected by misspecification. An alternative is suggested in this paper to obtain a valid covariance from a nonparametric estimator through the Fourier series tool, which involves two issues: estimation of the Fourier coefficients and selection of the truncation point to determine the number of terms in the Fourier expansion. Numerical studies for simulated data have been conducted to illustrate the performance of this approach. In addition, an application to a real environmental data set is included, related to the presence of nitrate in groundwater in Beja District (Portugal), so that pollution maps of the region are generated by solving the kriging equations with the use of the Fourier series estimates of the covariance.

Keywords

Covariance function Fourier series Kriging Truncation point 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Pilar García-Soidán
    • 1
  • Raquel Menezes
    • 2
  • Óscar Rubiños-López
    • 3
  1. 1.Department of Statistics and Operations ResearchUniversity of VigoPontevedraSpain
  2. 2.Department of Mathematics and ApplicationsUniversity of MinhoGuimarãesPortugal
  3. 3.Department of Signal Theory and CommunicationsUniversity of VigoVigoSpain

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