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April 2017 Consistency of likelihood estimation for Gibbs point processes
David Dereudre, Frédéric Lavancier
Ann. Statist. 45(2): 744-770 (April 2017). DOI: 10.1214/16-AOS1466

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.

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David Dereudre. Frédéric Lavancier. "Consistency of likelihood estimation for Gibbs point processes." Ann. Statist. 45 (2) 744 - 770, April 2017. https://doi.org/10.1214/16-AOS1466

Information

Received: 1 April 2015; Revised: 1 March 2016; Published: April 2017
First available in Project Euclid: 16 May 2017

zbMATH: 1371.62021
MathSciNet: MR3650399
Digital Object Identifier: 10.1214/16-AOS1466

Subjects:
Primary: 60D05 , 60G55 , 62F12 , 62M30

Keywords: area-interaction model , Lennard–Jones model , Parametric estimation , Strauss model , Variational principle

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 2 • April 2017
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