Search

Modelling the first-order intensity function is one of the main aims in point process theory, and it has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate. In the recent literature, estimation theory and several applications have been developed assuming this model, but without formally checking this assumption. In this paper we address this problem for a non-homogeneous Poisson point process, by proposing a new test based on an $L^2$-distance. We also prove the asymptotic normality of the statistic and we suggest a bootstrap procedure to accomplish the calibration. Two applications with real data are presented and a simulation study to better understand the performance of our proposals is accomplished. Finally some possible extensions of the present work to non-Poisson processes and to a multi-dimensional covariate context are detailed., Comment: 30 pages (23 main doc + 7 appendix); 9 figures; 3 tables

In the spatial point process context, kernel intensity estimation has been mainly restricted to exploratory analysis due to its lack of consistency. Different methods have been analysed to overcome this problem, and the inclusion of covariates resulted to be one possible solution. In this paper we focus on de\-fi\-ning a theoretical framework to derive a consistent kernel intensity estimator using covariates, as well as a consistent smooth bootstrap procedure. We define two new data-driven bandwidth selectors specifically designed for our estimator: a rule-of-thumb and a plug-in bandwidth based on our consistent bootstrap method. A simulation study is accomplished to understand the performance of our proposals in finite samples. Finally, we describe an application to a real data set consisting of the wildfires in Canada during June 2015, using meteorological information as covariates., Comment: 32 pages, 7 figures (15 images), 4 tables