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arXiv · 2309.12834

A functional central limit theorem for the K-function with an estimated intensity function

Anne Marie Svane·Christophe Biscio·Rasmus Waagepetersen
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Abstract

The $K$-function is arguably the most important functional summary statistic for spatial point processes. It is used extensively for goodness-of-fit testing and in connection with minimum contrast estimation for parametric spatial point process models. It is thus pertinent to understand the asymptotic properties of estimates of the $K$-function. In this paper we derive the functional asymptotic distribution for the $K$-function estimator. Contrary to previous papers on functional convergence we consider the case of an inhomogeneous intensity function. We moreover handle the fact that practical $K$-function estimators rely on plugging in an estimate of the intensity function. This removes two serious limitations of the existing literature.

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Anne Marie Svane, Christophe Biscio, Rasmus Waagepetersen. 2023-09-22. A functional central limit theorem for the K-function with an estimated intensity function. https://arxiv.org/abs/2309.12834

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