Orthogonal series estimation of the pair correlation function of a spatial point process

Abdollah Jalilian, Yongtao Guan, Rasmus Waagepetersen

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The pair correlation function is a fundamental spatial point process characteristic that, given the intensity function, determines second order moments of the point process. Non-parametric estimation of the pair correlation function is a typical initial step of a statistical analysis of a spatial point pattern. Kernel estimators are popular but especially for clustered point patterns suffer from bias for small spatial lags. In this paper we introduce an orthogonal series non-parametric estimator. It is consistent and asymptotically normal according to our theoretical and simulation results. In our simulations the new estimator outperforms the kernel estimators, in particular for Poisson and clustered point processes.

Original languageEnglish (US)
Pages (from-to)769-787
Number of pages19
JournalStatistica Sinica
Volume29
Issue number2
DOIs
StatePublished - Jan 1 2019

Fingerprint

Spatial Point Process
Orthogonal Series
Pair Correlation Function
Kernel Estimator
Point Process
Spatial Point Pattern
Intensity Function
Nonparametric Estimator
Nonparametric Estimation
Statistical Analysis
Siméon Denis Poisson
Simulation
Moment
Estimator
Series estimation
Point process
Kernel estimator

Keywords

  • Asymptotic normality
  • Consistency
  • Kernel estimator
  • Orthogonal series estimator
  • Pair correlation function
  • Spatial point process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Orthogonal series estimation of the pair correlation function of a spatial point process. / Jalilian, Abdollah; Guan, Yongtao; Waagepetersen, Rasmus.

In: Statistica Sinica, Vol. 29, No. 2, 01.01.2019, p. 769-787.

Research output: Contribution to journalArticle

Jalilian, Abdollah ; Guan, Yongtao ; Waagepetersen, Rasmus. / Orthogonal series estimation of the pair correlation function of a spatial point process. In: Statistica Sinica. 2019 ; Vol. 29, No. 2. pp. 769-787.
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