Significance tests for covariate-dependent trends in inhomogeneous spatio-temporal point processes

Modeling and inference for spatial and spatio-temporal point processes is an issue that has been broadly investigated in the last years. Application fields such as forestry, epidemiology and ecology have been the main engine driving such raised interest. The inclusion of spatially varying covariates in the models for the intensity function is becoming of particular interest, but little attention has been paid to testing the significance of such covariates. Testing the significance of covariates is important if one seeks to explain which covariates have an effect in the spatial or spatio-temporal distribution of the point pattern observed. We thus provide practical procedures to build statistical tests of significance for covariates that have an effect on the intensity function of a point pattern. Our approximation focuses on the conditional intensity function, by considering nonparametric kernel-based estimators. We calculate thinning probabilities under the conditions of absence and presence of a covariate and compare them through divergence measures. Based on Monte Carlo experiments, we approximate the statistical properties of our tests under a variety of practical scenarios. An application on testing the significance of a covariate in a spatio-temporal data set on wildfires is also developed.