Parameter Estimation for Inhomogeneous Space-Time Shot-Noise Cox Point Processes

We consider the problem of parameter estimation for inhomogeneous space-time shot-noise Cox point processes. We explore the possibility of using a stepwise estimation method and dimensionality-reducing techniques to estimate different parts of the model separately. We discuss the estimation method using projection processes and propose arefined method that avoids projection to the temporal domain. This remedies the main flaw of the method using projection processes - possible overlapping in the projection process of clusters, which are clearly separated in the original space-time process. This issue is more prominent in the temporal projection process where the amount of information lost by projection is higher than in the spatial projection process. For the refined method, we derive consistency and asymptotic normality results under the increasing domain asymptotics and appropriate moment and mixing assumptions. We also present asimulation study that suggests that cluster overlapping is successfully overcome by the refined method.