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

2021/09/28 by Biscio, Christophe A. N., Svane, Anne Marie
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2109.13741

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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