A functional central limit theorem for the K-function with an estimated intensity function
Statistics Theory
2023-09-25 v1 Statistics Theory
Abstract
The -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 -function. In this paper we derive the functional asymptotic distribution for the -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 -function estimators rely on plugging in an estimate of the intensity function. This removes two serious limitations of the existing literature.
Cite
@article{arxiv.2309.12834,
title = {A functional central limit theorem for the K-function with an estimated intensity function},
author = {Anne Marie Svane and Christophe Biscio and Rasmus Waagepetersen},
journal= {arXiv preprint arXiv:2309.12834},
year = {2023}
}
Comments
14 pages