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

Christophe A. N. Biscio; Anne Marie Svane

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arXiv · 2109.13741

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

Christophe A. N. Biscio·Anne Marie Svane

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Abstract

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.

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Christophe A. N. Biscio, Anne Marie Svane. 2021-09-28. A functional central limit theorem for the empirical Ripley's K-function. https://arxiv.org/abs/2109.13741

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