SEMINAR: Statistics Seminar

In this talk we address asymptotic properties of Takacs- Fiksel estimator for exponential family models of Gibbs point process. We will concentrate mainly on the consistency which is based on a complicated identifiability problem. We will present it precisely and we will give some sufficient conditions to solve it.

One motivation of this work is the parametric estimation of Quermass model (generalisation of the Area process or the famous Widom- Rowlinson model). The parameters are the intensity z and a vector theta which defines the energy of the system via a linear combination of Minkowski functionals. In this setting the classical Likelihood or Pseudolikelihood procedures are not able to estimate the intensity parameter z. The Takacs-Fiksel procedure seems to be efficient. Some Simulations will be presented.

This work is a collaboration with J.-F. Coeurjolly (Grenoble, France) and F. Lavancier (Nantes, France)