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Pointwise density estimation on metric spaces and applications in seismology

Author

Listed:
  • G. Cleanthous

    (National University of Ireland, Maynooth)

  • Athanasios G. Georgiadis

    (Trinity College of Dublin)

  • P. A. White

    (Brigham Young University)

Abstract

We are studying the problem of estimating density in a wide range of metric spaces, including the Euclidean space, the sphere, the ball, and various Riemannian manifolds. Our framework involves a metric space with a doubling measure and a self-adjoint operator, whose heat kernel exhibits Gaussian behaviour. We begin by reviewing the construction of kernel density estimators and the related background information. As a novel result, we present a pointwise kernel density estimation for probability density functions that belong to general Hölder spaces. The study is accompanied by an application in Seismology. Precisely, we analyze a globally-indexed dataset of earthquake occurrence and compare the out-of-sample performance of several approximated kernel density estimators indexed on the sphere.

Suggested Citation

  • G. Cleanthous & Athanasios G. Georgiadis & P. A. White, 2025. "Pointwise density estimation on metric spaces and applications in seismology," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(2), pages 119-148, February.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:2:d:10.1007_s00184-024-00948-2
    DOI: 10.1007/s00184-024-00948-2
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