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2020 Nonparametric estimation of the pair correlation function of replicated inhomogeneous point processes
Ganggang Xu, Chong Zhao, Abdollah Jalilian, Rasmus Waagepetersen, Jingfei Zhang, Yongtao Guan
Electron. J. Statist. 14(2): 3730-3765 (2020). DOI: 10.1214/20-EJS1755


We consider the nonparametric estimation of the isotropic pair correlation function (PCF) of inhomogeneous point processes when replicates are available. Based on carefully designed estimating equations, two types of nonparametric estimators, i.e., the local polynomial estimator and the orthogonal series estimator, are proposed and studied. The proposed estimators circumvent the problems caused by the need for estimating the unknown intensity function for kernel smoothed PCF estimators and they are free of edge correction terms. Asymptotic properties are investigated for both estimators and valid point-wise confidence bands are derived. Finite sample performances of the proposed estimators are demonstrated by simulation as well as an application to the Sina Weibo posting data.


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Ganggang Xu. Chong Zhao. Abdollah Jalilian. Rasmus Waagepetersen. Jingfei Zhang. Yongtao Guan. "Nonparametric estimation of the pair correlation function of replicated inhomogeneous point processes." Electron. J. Statist. 14 (2) 3730 - 3765, 2020.


Received: 1 August 2019; Published: 2020
First available in Project Euclid: 12 October 2020

zbMATH: 07270276
MathSciNet: MR4161297
Digital Object Identifier: 10.1214/20-EJS1755

Primary: 60K35 , 60K35
Secondary: 60K35

Keywords: Confidence band , estimating equations , local polynomial estimator , nonparametric estimation , orthogonal series estimator , replicated point patterns


Vol.14 • No. 2 • 2020
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