Consistency of likelihood estimation for Gibbs point processes
David Dereudre, Frédéric Lavancier
The Annals of Statistics · 2017 · Volume 45 · Issue 2
Abstract
Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general. It includes pairwise pair potentials, finite and infinite multibody interactions and geometrical interactions, where the range can be finite or infinite. The Gibbs interaction may depend linearly or nonlinearly on the parameters, a particular case being hardcore parameters and interaction range parameters. As important examples, we deduce the consistency of the MLE for all parameters of the Strauss model, the hardcore Strauss model, the Lennard–Jones model and the area-interaction model.
Keywords
60D05, 60G55, 62F12, 62M30, area-interaction model, Lennard–Jones model, Parametric estimation, Strauss model, Variational principle
Enable JavaScript for citation tools and additional paper interactions.