Open Access
May 2017 Parametric estimation of pairwise Gibbs point processes with infinite range interaction
Jean-François Coeurjolly, Frédéric Lavancier
Bernoulli 23(2): 1299-1334 (May 2017). DOI: 10.3150/15-BEJ779


This paper is concerned with statistical inference for infinite range interaction Gibbs point processes, and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical statistical methodologies such as the pseudo-likelihood and the logistic regression methods, originally defined and studied for finite range models. Then we prove that the associated estimators are strongly consistent and satisfy a central limit theorem, provided the pairwise interaction function tends sufficiently fast to zero. To this end, we introduce a new central limit theorem for almost conditionally centered triangular arrays of random fields.


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Jean-François Coeurjolly. Frédéric Lavancier. "Parametric estimation of pairwise Gibbs point processes with infinite range interaction." Bernoulli 23 (2) 1299 - 1334, May 2017.


Received: 1 July 2015; Revised: 1 October 2015; Published: May 2017
First available in Project Euclid: 4 February 2017

zbMATH: 06701627
MathSciNet: MR3606767
Digital Object Identifier: 10.3150/15-BEJ779

Keywords: central limit theorem , Lennard–Jones potential , pseudo-likelihood

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 2 • May 2017
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