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 χ2χ2-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 χ2χ2-test is not conclusive in either case.