Test for the First-Order Stationarity for Spatial Point Processes in Arbitrary Regions

摘要

This article proposes a Kolmogorov-Smirnov type test for the first-order stationarity of spatial point processes in arbitrary regions, where the test statistic is derived by maximizing the absolute difference between the observed and expected counts of events. In order to derive the p-value using the asymptotic distribution, the maximization of the test statistic is only considered in a collection of subsets of the study region. By carefully considering the choice of the collection, we show that under the null hypothesis of stationarity the test statistic weakly converges the absolute maximum of the standard Brownian bridge. Therefore, the proposed method can be easily applied to assess the first-order stationarity of spatial point processes in a variety of geographical regions. According to our simulation and case studies, we conclude that our method is powerful in testing the first-order stationarity of spatial point processes in arbitrary regions.