Isotropy test for spatial point processes using stochastic reconstruction

We develop a model-free isotropy test for spatial point patterns. The proposed test statistic assesses the discrepancy between the uniform distribution and the empirical normalised reduced second-order moment measure of a sector of increasing central angle. The null distribution of the test statistic is approximated by the empirical distribution obtained from bootstrap-type samples, which are generated by a stochastic procedure reconstructing independent isotropic patterns that resemble the spatial structure of the given point pattern, without specifying any underlying model. Simulation studies show that, when compared with the asymptotic χ²-test by Guan et al. (2006), the powers of the proposed test are more robust to different choices of user-chosen parameter. When applied to patterns of amacrine cells and Spanish towns, the bootstrap-type test clearly suggests rejection for the former and not rejection for the latter, while the asymptotic χ²-test is not conclusive in either case.