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

8Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

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.

Cite

CITATION STYLE

APA

Xu, G., Zhao, C., Jalilian, A., Waagepetersen, R., Zhang, J., & Guan, Y. (2020). Nonparametric estimation of the pair correlation function of replicated inhomogeneous point processes. Electronic Journal of Statistics, 14(2), 3730–3765. https://doi.org/10.1214/20-EJS1755

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free