Testing for spatial stationarity in point patterns

Abstract

A common assumption while analyzing spatial point processes is translation and rotation invariance. However, in many practical situations nonstationarity is a more plausible assumption. Considering that second-order methods provide a natural starting point for the analysis of spatial point process data, we propose a formal nonparametric approach to test for stationarity based on a wide range of possible estimators for the first-order intensity function and the reduced second moment measure. We demonstrate the efficacy of the approach through simulation studies and real applications.