Nonparametric estimation of the pair correlation function of replicated inhomogeneous point processes

Ganggang Xu, Chong Zhao, Abdollah Jalilian, Rasmus Waagepetersen, Jingfei Zhang, Yongtao Guan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)3730-3765
Number of pages36
JournalElectronic Journal of Statistics
Volume14
Issue number2
DOIs
StatePublished - 2020

Keywords

  • Confidence band
  • Estimating equations
  • Local polynomial estimator
  • Nonparametric estimation
  • Orthogonal series estimator
  • Replicated point patterns

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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