Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes

Dvořák, Jiří; Prokešová, Michaela

doi:10.1007/s10492-016-0138-6

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…Conditions C1-C3 are mild conditions commonly used in point process literature, see, e.g., Dvořák and Prokešová (2016); Coeurjolly et al (2017). Condition C4 assumes that the kernel function should have a bounded support such as the popular uniform and Epanechnikov kernel functions.…”

Section: The Local Polynomial Estimatormentioning

confidence: 99%

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

Xu¹,

Zhao²,

Jalilian³

et al. 2020

Electron. J. Statist.

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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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Section: The Local Polynomial Estimatormentioning

confidence: 99%

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

Xu¹,

Zhao²,

Jalilian³

et al. 2020

Electron. J. Statist.

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“…the discussions in Waagepetersen and Guan (2009) and Coeurjolly and Møller (2014). The condition N3 is difficult to verify and is usually left as an assumption, see Waagepetersen and Guan (2009), Coeurjolly and Møller (2014) and Dvořák and Prokešová (2016). However, at least in the stationary case, and in case of estimation ofθ k,n , the expression for var(θ k,n ) in Section S2 of the supplementary material shows that τ 2 n = |W n |var(θ k,n ) converges to a constant which supports the plausibility of condition N3.…”

Section: Asymptotic Normalitymentioning

confidence: 99%

Orthogonal Series Estimation of the Pair Correlation Function of a Spatial Point Process

Jalilian¹,

Guan²,

Waagepetersen³

2019

STAT SINICA

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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 a new orthogonal series estimator. The new estimator is consistent and asymptotically normal according to our theoretical and simulation results. Our simulations further show that the new estimator can outperform the kernel estimators in particular for Poisson and clustered point processes.

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Fundamental problems in fitting spatial cluster process models

et al. 2022

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Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes

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Cited by 3 publications

References 18 publications

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

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

Orthogonal Series Estimation of the Pair Correlation Function of a Spatial Point Process

Fundamental problems in fitting spatial cluster process models

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