A functional central limit theorem for the empirical Ripley's K-function

We establish a functional central limit theorem for Ripley's K-function for two classes of point processes. One is the class of point processes having exponential decay of correlations and further satisfying a conditional m-dependence condition. The other is a family of Gibbs point processes. W...

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Bibliographic Details
Published in:arXiv.org 2021-09
Main Authors: Biscio, Christophe A N, Svane, Anne Marie
Format: Article
Language:English
Subjects:
Goodness of fit
Statistical tests
Theorems
Online Access:Get full text
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Summary:We establish a functional central limit theorem for Ripley's K-function for two classes of point processes. One is the class of point processes having exponential decay of correlations and further satisfying a conditional m-dependence condition. The other is a family of Gibbs point processes. We illustrate the use of our theorem for goodness-of-fit tests in simulations.
ISSN:2331-8422