Testing for signif cant differences between two spatial patterns using covariates

Abstract

This paper addresses the problem of comparing the spatial distribution of two point patterns. A formal statistical test is proposed to decide whether two observed patterns share the same theoretical intensity model. This underlying model assumes that the first-order intensity function of the process generating the patterns may depend on covariate information. The test statistic consists of an $L_2$-distance between two kernel estimators for the corresponding relative density, which is shown to be asymptotically normal under the null hypothesis assuming that the underlying process is Poisson. In practice a suitable bootstrap method is proposed to calibrate the test. Simulations are used to explore the ability of the proposed test to identify different spatial patterns. An application to the analysis of wildfires in Canada shows the practicality of the proposal, with appealing conclusions regarding to the need of including covariate information