Globally intensity-reweighted estimators for K- and pair correlation functions

Thomas Shaw; Jesper Møller; Rasmus Plenge Waagepetersen

doi:10.1111/anzs.12318

Globally intensity-reweighted estimators for K- and pair correlation functions

Thomas Shaw, Jesper Møller^*, Rasmus Plenge Waagepetersen

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6 Citationer (Scopus)

Abstract

We introduce new estimators of the inhomogeneous K-function and the pair correlation function of a spatial point process as well as the cross K-function and the cross pair correlation function of a bivariate spatial point process under the assumption of second-order intensity-reweighted stationarity. These estimators rely on a ‘global’ normalisation factor which depends on an aggregation of the intensity function, while the existing estimators depend ‘locally’ on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study.

Originalsprog	Engelsk
Tidsskrift	Australian and New Zealand Journal of Statistics
Vol/bind	63
Udgave nummer	1
Sider (fra-til)	93-118
Antal sider	26
ISSN	1369-1473
DOI	https://doi.org/10.1111/anzs.12318
Status	Udgivet - mar. 2021

Bibliografisk note

Funding Information:
The first author was supported by grants from the U.S. National Science Foundation (MCB1552439) and National Institutes of Health (R01GM129347) and he thanks his advisor Dr. Sarah Veatch for her support. The last two authors were supported by the ?Danish Council for Independent Research ? Natural Sciences? grant DFF ? 7014-00074 ?Statistics for point processes in space and beyond?, and by the ?Centre for Stochastic Geometry and Advanced Bioimaging? funded by grant 8721 from the Villum Foundation.

Funding Information:
The first author was supported by grants from the U.S. National Science Foundation (MCB1552439) and National Institutes of Health (R01GM129347) and he thanks his advisor Dr. Sarah Veatch for her support. The last two authors were supported by the ‘Danish Council for Independent Research — Natural Sciences’ grant DFF – 7014‐00074 ‘Statistics for point processes in space and beyond’, and by the ‘Centre for Stochastic Geometry and Advanced Bioimaging’ funded by grant 8721 from the Villum Foundation.

Publisher Copyright:
© 2021 John Wiley & Sons Australia, Ltd

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10.1111/anzs.12318

http://arxiv.org/pdf/2004.00527

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Citationsformater

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title = "Globally intensity-reweighted estimators for K- and pair correlation functions",

abstract = "We introduce new estimators of the inhomogeneous K-function and the pair correlation function of a spatial point process as well as the cross K-function and the cross pair correlation function of a bivariate spatial point process under the assumption of second-order intensity-reweighted stationarity. These estimators rely on a {\textquoteleft}global{\textquoteright} normalisation factor which depends on an aggregation of the intensity function, while the existing estimators depend {\textquoteleft}locally{\textquoteright} on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study.",

keywords = "inhomogeneous K-function, intensity function, kernel estimation, pair correlation function, second-order intensity-reweighted stationarity, spatial point process",

author = "Thomas Shaw and Jesper M{\o}ller and Waagepetersen, {Rasmus Plenge}",

note = "Publisher Copyright: {\textcopyright} 2021 John Wiley & Sons Australia, Ltd",

year = "2021",

month = mar,

doi = "10.1111/anzs.12318",

language = "English",

volume = "63",

pages = "93--118",

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T1 - Globally intensity-reweighted estimators for K- and pair correlation functions

AU - Shaw, Thomas

AU - Møller, Jesper

AU - Waagepetersen, Rasmus Plenge

PY - 2021/3

Y1 - 2021/3

N2 - We introduce new estimators of the inhomogeneous K-function and the pair correlation function of a spatial point process as well as the cross K-function and the cross pair correlation function of a bivariate spatial point process under the assumption of second-order intensity-reweighted stationarity. These estimators rely on a ‘global’ normalisation factor which depends on an aggregation of the intensity function, while the existing estimators depend ‘locally’ on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study.

AB - We introduce new estimators of the inhomogeneous K-function and the pair correlation function of a spatial point process as well as the cross K-function and the cross pair correlation function of a bivariate spatial point process under the assumption of second-order intensity-reweighted stationarity. These estimators rely on a ‘global’ normalisation factor which depends on an aggregation of the intensity function, while the existing estimators depend ‘locally’ on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study.

KW - inhomogeneous K-function

KW - intensity function

KW - kernel estimation

KW - pair correlation function

KW - second-order intensity-reweighted stationarity

KW - spatial point process

UR - http://www.scopus.com/inward/record.url?scp=85105819470&partnerID=8YFLogxK

U2 - 10.1111/anzs.12318

DO - 10.1111/anzs.12318

M3 - Journal article

AN - SCOPUS:85105819470

SN - 1369-1473

VL - 63

SP - 93

EP - 118

JO - Australian and New Zealand Journal of Statistics

JF - Australian and New Zealand Journal of Statistics

IS - 1

ER -

Globally intensity-reweighted estimators for K- and pair correlation functions

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