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On Some Characteristics of Gaussian Covariance Functions

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  • Sandra De Iaco
  • Donato Posa
  • Claudia Cappello
  • Sabrina Maggio

Abstract

The concepts of isotropy/anisotropy and separability/non‐separability of a covariance function are strictly related. If a covariance function is separable, it cannot be isotropic or geometrically anisotropic, except for the Gaussian covariance function, which is the only model both separable and isotropic. In this paper, some interesting results concerning the Gaussian covariance model and its properties related to isotropy and separability are given, and moreover, some examples are provided. Finally, a discussion on asymmetric models, with Gaussian marginals, is furnished and the strictly positive definiteness condition is discussed.

Suggested Citation

  • Sandra De Iaco & Donato Posa & Claudia Cappello & Sabrina Maggio, 2021. "On Some Characteristics of Gaussian Covariance Functions," International Statistical Review, International Statistical Institute, vol. 89(1), pages 36-53, April.
    • Handle: RePEc:bla:istatr:v:89:y:2021:i:1:p:36-53
    DOI: 10.1111/insr.12403
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    References listed on IDEAS

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    4. Huiyan Sang & Jianhua Z. Huang, 2012. "A full scale approximation of covariance functions for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 111-132, January.
    5. He, Heping & Severini, Thomas A., 2016. "A flexible approach to inference in semiparametric regression models with correlated errors using Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 316-329.
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