Open Access
2014 A Kolmogorov-Smirnov type test for independence between marks and points of marked point processes
Tonglin Zhang
Electron. J. Statist. 8(2): 2557-2584 (2014). DOI: 10.1214/14-EJS961


Marked point processes are commonly used stochastic models for representing a finite number of natural hazard events located in space and time, because these kinds of data often associate measurements (i.e. marks) with locations (i.e. points) of events. Methods of marked point processes when marks and points are interacting have been proposed, but it is still necessary to know whether the interaction must be considered. This article presents a Kolmogorov-Smirnov type method to test the independence between points and marks of marked point processes. The asymptotic distribution of the test statistic under a few weak regularity conditions is derived. According to the asymptotic result, a specific way to construct the test statistic is recommended as its null distribution can be approximated by the absolute maximum of the two-dimensional standard Brownian pillow. The simulation results and real data analyses demonstrated that the proposed method is powerful in detecting weak dependence between marks and points and performs well with a moderate sample size.


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Tonglin Zhang. "A Kolmogorov-Smirnov type test for independence between marks and points of marked point processes." Electron. J. Statist. 8 (2) 2557 - 2584, 2014.


Published: 2014
First available in Project Euclid: 9 December 2014

zbMATH: 1309.62157
MathSciNet: MR3285876
Digital Object Identifier: 10.1214/14-EJS961

Primary: 62M30
Secondary: 62G10, 62G20

Keywords: asymptotic distribution , Brownian pillow and Brownian sheet , Convergence in distribution , Empirical processes , independence between points and marks , Kolmogorov-Smirnov type test , marked point processes

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 2 • 2014
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