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

2023/09/22 by Anne Marie Svane, Svane, Anne Marie, Christophe A. N. Biscio +3
Economics, Econometrics and Finance · Mathematics · #60F05 (Secondary) #60F17 (Primary) 60G55 #Economic and Environmental Valuation #FOS: Mathematics #Point processes and geometric inequalities #Spatial and Panel Data Analysis #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2309.12834

openalex publication_date 2023/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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