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Convergence arguments to bridge cauchy and matérn covariance functions

Author

Listed:
  • Tarik Faouzi

    (Universidad de Santiago de Chile)

  • Emilio Porcu

    (Khalifa University
    Trinity College Dublin)

  • Igor Kondrashuk

    (Universidad del Bío-Bío)

  • Moreno Bevilacqua

    (Universidad Adolfo Ibañez
    Ca’ Foscari University of Venice)

Abstract

The Matérn and the Generalized Cauchy families of covariance functions have a prominent role in spatial statistics as well as in a wealth of statistical applications. The Matérn family is crucial to index mean-square differentiability of the associated Gaussian random field; the Cauchy family is a decoupler of the fractal dimension and Hurst effect for Gaussian random fields that are not self-similar. Our effort is devoted to prove that a scale-dependent family of covariance functions, obtained as a reparameterization of the Generalized Cauchy family, converges to a particular case of the Matérn family, providing a somewhat surprising bridge between covariance models with light tails and covariance models that allow for long memory effect.

Suggested Citation

  • Tarik Faouzi & Emilio Porcu & Igor Kondrashuk & Moreno Bevilacqua, 2024. "Convergence arguments to bridge cauchy and matérn covariance functions," Statistical Papers, Springer, vol. 65(2), pages 645-660, April.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:2:d:10.1007_s00362-023-01400-9
    DOI: 10.1007/s00362-023-01400-9
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    References listed on IDEAS

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