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

Author

Listed:
  • Arafat, Ahmed
  • Gregori, Pablo
  • Porcu, Emilio

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.

Suggested Citation

  • Arafat, Ahmed & Gregori, Pablo & Porcu, Emilio, 2020. "Schoenberg coefficients and curvature at the origin of continuous isotropic positive definite kernels on spheres," Statistics & Probability Letters, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:stapro:v:156:y:2020:i:c:s0167715219302640
    DOI: 10.1016/j.spl.2019.108618
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