Convergence arguments to bridge cauchy and matérn covariance functions

Tarik Faouzi, Emilio Porcu (), Igor Kondrashuk and Moreno Bevilacqua
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Tarik Faouzi: Universidad de Santiago de Chile
Emilio Porcu: Khalifa University
Igor Kondrashuk: Universidad del Bío-Bío
Moreno Bevilacqua: Universidad Adolfo Ibañez

Statistical Papers, 2024, vol. 65, issue 2, No 5, 645-660

Abstract: 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.

Keywords: Mellin–Barnes transforms; Positive definite; Spectral densities; Random field (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01400-9

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