Consistency of likelihood estimation for Gibbs point processes

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 non-linearly 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download
Contributor : Frédéric Lavancier <>
Submitted on : Monday, January 25, 2016 - 5:06:35 PM
Last modification on : Tuesday, July 23, 2019 - 1:00:04 PM
Long-term archiving on : Tuesday, April 26, 2016 - 11:36:32 AM


Files produced by the author(s)


  • HAL Id : hal-01144877, version 2
  • ARXIV : 1506.02887



David Dereudre, Frédéric Lavancier. Consistency of likelihood estimation for Gibbs point processes. Annals of Statistics, Institute of Mathematical Statistics, 2016. ⟨hal-01144877v2⟩



Record views


Files downloads