In this contribution we consider the problem of testing possible dependence between a point process and a spatial covariate. We recall the available methods which are based on the assumption of a Poisson process.
Taking advantage of the recent development of the random shift methods we study the nonparametric tests using random shifts which are suitable also for non-Poisson processes. We study the performance of the different tests in a simulation study and conclude that the random shift test, either with the toroidal correction or the variance correction, depending on the strength of interactions in the point process, performs well for non-Poisson processes.