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An approach for valid covariance estimation via the Fourier series

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Resumo: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.
Autores principais:García Soidán, Pilar
Outros Autores:Menezes, Raquel; Rubinos-Lopez, Oscar
Assunto:Covariance function Fourier series Kriging Truncation point
Ano:2012
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso restrito
Instituição associada:Universidade do Minho
Idioma:inglês
Origem:RepositóriUM - Universidade do Minho

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