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

TL;DR

This paper proves a functional central limit theorem for Ripley's K-function applicable to certain dependent point processes, enabling improved statistical testing methods in spatial analysis.

Contribution

It introduces a new functional CLT for Ripley's K-function for processes with exponential decay of correlations and Gibbs processes, expanding theoretical understanding.

Findings

The theorem applies to processes with exponential decay of correlations.

It extends to Gibbs point processes.

Demonstrates practical use in goodness-of-fit tests.

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.