Pointwise density estimation on metric spaces and applications in seismology

Galatia Cleanthous; Athanasios G. Georgiadis; Philip A. White

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arXiv · 2304.00085

Pointwise density estimation on metric spaces and applications in seismology

Galatia Cleanthous·Athanasios G. Georgiadis·Philip A. White

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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 H\"{o}lder 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.

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Galatia Cleanthous, Athanasios G. Georgiadis, Philip A. White. 2023-03-31. Pointwise density estimation on metric spaces and applications in seismology. https://arxiv.org/abs/2304.00085

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