On minimum Lp-distance estimation for inhomogeneous Poisson processes

We consider the problem of parameter estimation by the observations of the inhomogeneous Poisson processes. We suppose that the intensity function of these processes is a smooth function of the unknown parameter and as a method of estimation we take the minimum distance approach. We are interested by the behavior of estimators in non Hilbertian situation and we define the minimum distance estimation (MDE) with the help of the L-p metrics. We show that (under regularity conditions) the MDE is consistent and we describe its limit distribution.