A functional central limit theorem for the K-function with an estimated intensity function
Copyright policy )A functional central limit theorem for the K-function with an estimated intensity function
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.
14 pages
Functional limit theorems; invariance principles, 60F17 (Primary) 60G55, 60F05 (Secondary), functional central limit theorem, Ripley's \(K\)-function, Central limit and other weak theorems, Mathematics - Statistics Theory, Statistics Theory (math.ST), intensity estimation, inhomogeneous \(K\)-function, goodness-of-fit test, FOS: Mathematics, Point processes (e.g., Poisson, Cox, Hawkes processes), point process
Functional limit theorems; invariance principles, 60F17 (Primary) 60G55, 60F05 (Secondary), functional central limit theorem, Ripley's \(K\)-function, Central limit and other weak theorems, Mathematics - Statistics Theory, Statistics Theory (math.ST), intensity estimation, inhomogeneous \(K\)-function, goodness-of-fit test, FOS: Mathematics, Point processes (e.g., Poisson, Cox, Hawkes processes), point process
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