The Annals of Statistics
- Ann. Statist.
- Volume 45, Number 2 (2017), 744-770.
Consistency of likelihood estimation for Gibbs point processes
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.
Ann. Statist., Volume 45, Number 2 (2017), 744-770.
Received: April 2015
Revised: March 2016
First available in Project Euclid: 16 May 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Dereudre, David; Lavancier, Frédéric. Consistency of likelihood estimation for Gibbs point processes. Ann. Statist. 45 (2017), no. 2, 744--770. doi:10.1214/16-AOS1466. https://projecteuclid.org/euclid.aos/1494921956
- Supplement to “Consistency of likelihood estimation for Gibbs point processes”. This supplementary material provides the proofs of Lemma 4, Corollary 1, Theorems 2–4 and Propositions 1 and 2.