Pointwise density estimation on metric spaces and applications in seismology

IF 0.9 4区 数学 Q3 STATISTICS & PROBABILITY
Metrika Pub Date : 2024-02-13 DOI:10.1007/s00184-024-00948-2
G. Cleanthous, Athanasios G. Georgiadis, P. A. White
{"title":"Pointwise density estimation on metric spaces and applications in seismology","authors":"G. Cleanthous, Athanasios G. Georgiadis, P. A. White","doi":"10.1007/s00184-024-00948-2","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"91 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Metrika","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00184-024-00948-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0

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.

Abstract Image

度量空间上的点式密度估计及其在地震学中的应用
我们正在研究各种度量空间中的密度估计问题,包括欧几里得空间、球体、球和各种黎曼流形。我们的框架涉及一个具有加倍度量和自联合算子的度量空间,其热核表现出高斯特性。我们首先回顾了核密度估计器的构造和相关背景信息。作为一项新成果,我们提出了属于一般赫尔德空间的概率密度函数的点核密度估计。研究还附带了地震学中的一个应用。确切地说,我们分析了一个全局索引的地震发生数据集,并比较了在球面上索引的几个近似核密度估计器的样本外性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Metrika
Metrika 数学-统计学与概率论
CiteScore
1.50
自引率
14.30%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Metrika is an international journal for theoretical and applied statistics. Metrika publishes original research papers in the field of mathematical statistics and statistical methods. Great importance is attached to new developments in theoretical statistics, statistical modeling and to actual innovative applicability of the proposed statistical methods and results. Topics of interest include, without being limited to, multivariate analysis, high dimensional statistics and nonparametric statistics; categorical data analysis and latent variable models; reliability, lifetime data analysis and statistics in engineering sciences.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信