In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on asymptotics or on Monte Carlo simulation of a parametric null model. Here, we present a nonparametric test based on resampling the Fry points of the observed point pattern. Empirical levels and powers of the test are investigated in a simulation study for four point process models with anisotropy induced by different mechanisms. Finally, a real data set is tested for isotropy.

翻译：在空间统计学中，点过程通常被假定为各向同性，即其分布在旋转下保持不变。文献中关于各向同性的零假设统计检验要么基于渐近理论，要么基于参数化零模型的蒙特卡洛模拟。本文提出一种基于重采样观测点模式Fry点的非参数检验方法。通过模拟研究，针对四种由不同机制诱导各向异性的点过程模型，检验了该方法的经验水平和功效。最后，对一组真实数据集进行了各向同性检验。