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Mathematical Genesis of the Spatio-Temporal Covariance Functions

  • Fernández-Avilés, G
  • Montero, JM
  • Mateu, J

Obtaining new and flexible classes of nonseparable spatio-temporal covariances have resulted in a key point of research in the last years within the context of spatiotemporal Geostatistics. Approach: In general, the literature has focused on the problem of full symmetry and the problem of anisotropy has been overcome. Results: By exploring mathematical properties of positive definite functions and their close connection to covariance functions we are able to develop new spatio-temporal covariance models taking into account the problem of spatial anisotropy. Conclusion/Recommendations: The resulting structures are proved to have certain interesting mathematical properties, together with a considerable applicability.

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File URL: http://mpra.ub.uni-muenchen.de/35874/1/MPRA_paper_35874.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 35874.

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Date of creation: 2011
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Publication status: Published in Journal of Mathematics and Statistics 7.1(2011): pp. 37-44
Handle: RePEc:pra:mprapa:35874
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  1. Porcu, Emilio & Mateu, Jorge & Christakos, George, 2009. "Quasi-arithmetic means of covariance functions with potential applications to space-time data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1830-1844, September.
  2. Michael L. Stein, 2005. "Space-Time Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 310-321, March.
  3. Montserrat Fuentes, 2002. "Spectral methods for nonstationary spatial processes," Biometrika, Biometrika Trust, vol. 89(1), pages 197-210, March.
  4. P. Gregori & E. Porcu & J. Mateu & Z. Sasvári, 2008. "On potentially negative space time covariances obtained as sum of products of marginal ones," Annals of the Institute of Statistical Mathematics, Springer, vol. 60(4), pages 865-882, December.
  5. Gneiting T., 2002. "Nonseparable, Stationary Covariance Functions for Space-Time Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 590-600, June.
  6. Mitchell, Matthew W. & Genton, Marc G. & Gumpertz, Marcia L., 2006. "A likelihood ratio test for separability of covariances," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1025-1043, May.
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