Test for Stationarity for Spatial Point Processes in Arbitrary Regions

• Activity Number: 254
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Bingrou Zhou*+ and Tonglin Zhang
• Companies: and Purdue University
• Keywords: Stationarity ; Spatial ; Statistics

Abstract

We propose a Kolmogorov-Smirnov type test for stationarity for 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 by using the asymptotic distribution, the maximization of the test statistic is only considered in a subset of the study region. For a special choice of the subset, the null distribution of the test statistic may weakly converge to the absolute maximum of the standard Brownian bridge. Therefore, the proposed method can be easily applied to test stationarity for spatial point processes in a variety of geographical regions. According to our simulation and case studies, we conclude that our method is effective in testing stationarity for spatial point processes in arbitrary regions.