Statistics for Inhomogeneous Space-Time Shot-Noise Cox Processes

In the paper we introduce a flexible inhomogeneous space-time shot-noise Cox process model and derive a two-step estimation procedure for it. In the first step the inhomogeneity is estimated by means of a Poisson score estimating equation and in the second step we use minimum contrast estimation based on second order properties to obtain estimates of the clustering parameters. The suggested model is not separable but it has a special interaction structure which enables to use the spatial and temporal projections of the process for parameter estimation. Efficiency of the introduced method is investigated by means of a simulation study and it is compared to a previously used method.