Independent component models for replicated point processes

Abstract

We propose a semiparametric independent-component model for the intensity functions of replicated point processes. We show that the maximum likelihood estimators of the model parameters are consistent and asymptotically normal when the number of replications goes to infinity. The finite-sample behavior of the estimators is studied by simulation. As an example of application, we analyze the temporal variation in the spatial distribution of street robberies in Chicago.