Testing the zonal stationarity of spatial point processes: applied to prostate tissues and trees locations

This work aims to test the second-order stationarity of a spatial point pattern based on the local spectra concept. Using a logarithmic transformation, the mechanism of the proposed test becomes approximately identical to a simple two factor analysis of variance with the known variance of the noise term. This procedure can be also used for testing the stationarity in the neighborhood of a particular point of the observation window. The same idea is used in post-hoc tests to cluster the point pattern into stationary and non-stationary sub-windows. The performance of the proposed method is examined through a simulation study and is then applied to a practical data. The proposed test shows a considerable empirical power and satisfactorily empirical size.