Pointwise density estimation on metric spaces and applications in seismology

G. Cleanthous (), Athanasios G. Georgiadis () and P. A. White ()
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G. Cleanthous: National University of Ireland, Maynooth
Athanasios G. Georgiadis: Trinity College of Dublin
P. A. White: Brigham Young University

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 2, No 1, 119-148

Abstract: 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.

Keywords: Ahlfors regularity; Doubling volume; Density estimation; Out-of-sample performance; Pointwise estimation; Seismology; Primary 62G07; Secondary 58J35; 58Z05; 43A85 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-024-00948-2

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