Pointwise density estimation on metric spaces and applications in seismology

2023/03/31 by Galatia Cleanthous, Cleanthous, Galatia, Athanasios G. Georgiadis +3 · 1 citation
Computer Science · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Morphological variations and asymmetry #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2304.00085

openalex publication_date 2023/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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