An approach for valid covariance estimation via the Fourier series |
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Authors: | Pilar García-Soidán Raquel Menezes Óscar Rubiños-López |
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Institution: | 1.Department of Statistics and Operations Research,University of Vigo,Pontevedra,Spain;2.Department of Mathematics and Applications,University of Minho,Guimar?es,Portugal;3.Department of Signal Theory and Communications,University of Vigo,Vigo,Spain |
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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. |
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