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 L(2) 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 chi(2) 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.
Guan
Yongtao
Y
Department of Management Science, University of Miami, Coral Gables, Florida 33124-6544, USA. yguan@miami.edu
Sherman
Michael
M
Calvin
James A
JA
D016880:Anisotropy; D016009:Chi-Square Distribution; D003198:Computer Simulation; D003889:Desert Climate; D004463:Ecology / Q000379:methods / Q000706:statistics & numerical data; D010944:Plants; D018709:Statistics, Nonparametric