Schoenberg coefficients and curvature at the origin of continuous isotropic positive definite kernels on spheres

Ahmed Arafat, Pablo Gregori and Emilio Porcu

Statistics & Probability Letters, 2020, vol. 156, issue C

Abstract: We consider the class Ψd of continuous functions that define isotropic covariance functions in the d-dimensional sphere Sd. We provide a new recurrence formula for the solution of Problem 1 in Gneiting (2013b), solved by Fiedler (2013). In addition, we have improved the current bounds for the curvature at the origin of locally supported covariances (Problem 3 in Gneiting (2013b)), which is of applied interest at least for d=2.

Keywords: Positive definite kernel; Schoenberg coefficients; Gegenbauer polynomials; Isotropic covariance function (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2019.108618

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