Assessing isotropy for spatial point processes

A common assumption while analyzing spatial point processes is direction invariance, i.e., isotropy. In this article, we propose a formal nonparametric approach to test for isotropy based on the asymptotic joint normality of the sample second-order intensity function. We derive an L₂ consistent subsampling estimator for the asymptotic covariance matrix of the sample second-order intensity function and use this to construct a test statistic with a χ² limiting distribution. We demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set, where our approach confirms suspected directional effects in the spatial distribution of the desert plant species.