Spatio-temporal point patterns on linear networks: Pseudo-separable intensity estimation

Abstract

Aside from reviewing different intensity estimation schemesfor point processes on linear networks, this paper introducestwo Voronoi-based intensity estimation approaches for spatio-temporal linear network point processes. The first is a separableestimator, which is obtained as a scaled product of a resample-smoothed Voronoi intensity estimator on the linear network inquestion and another one on the time domain. The second one,which we refer to as a pseudo-separable resample-smoothedVoronoi intensity estimator, uses a slightly different thinningstrategy.Throughasimulationstudyweshowthatthelatterper-forms slightly better than the former. We finally apply the latterestimator to a spatio-temporal traffic accident point pattern.