An approach for valid covariance estimation via the Fourier series
2012
García Soidán, Pilar | Menezes, Raquel | Rubinos-Lopez, Oscar
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 itmay be affected by misspecification. An alternative is suggested in this paper to obtain avalid 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 realenvironmental 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.
Show more [+] Less [-]Universidade do Minho. Centro de Investigação de Matemática (CMAT)
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