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Fitting negative spatial covariances to geothermal field temperatures in Nea Kessani (Greece)
Author(s) -
Mateu Jorge,
Porcu Emilio,
Christakos George,
Bevilacqua Moreno
Publication year - 2007
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.871
Subject(s) - covariance , covariance function , geothermal gradient , econometrics , field (mathematics) , statistics , mathematics , spatial dependence , set (abstract data type) , goodness of fit , computer science , geology , geophysics , pure mathematics , programming language
In this paper, we investigate the problem of negative empirical covariances for temperature data in a three‐dimensional geothermal field. We make use of permissibility criteria that allow a linear combination of covariance functions to be positive definite even if some of the weights of the linear combination are set to be negative. We thus propose a generalized sum of spatial covariance structures to model negative spatial covariances. We evaluate the performance of the proposed model, together with that of other celebrated, and widely used covariance functions. Comparison is done in terms of cross‐validation, which allows to evaluate the relative bias, accuracy of estimation, and goodness‐of‐fit. Copyright © 2007 John Wiley & Sons, Ltd.