Bernoulli
- Bernoulli
- Volume 23, Number 2 (2017), 1299-1334.
Parametric estimation of pairwise Gibbs point processes with infinite range interaction
Jean-François Coeurjolly and Frédéric Lavancier
Abstract
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.
Article information
Source
Bernoulli, Volume 23, Number 2 (2017), 1299-1334.
Dates
Received: July 2015
Revised: October 2015
First available in Project Euclid: 4 February 2017
Permanent link to this document
https://projecteuclid.org/euclid.bj/1486177400
Digital Object Identifier
doi:10.3150/15-BEJ779
Mathematical Reviews number (MathSciNet)
MR3606767
Zentralblatt MATH identifier
06701627
Keywords
central limit theorem Lennard–Jones potential pseudo-likelihood
Citation
Coeurjolly, Jean-François; Lavancier, Frédéric. Parametric estimation of pairwise Gibbs point processes with infinite range interaction. Bernoulli 23 (2017), no. 2, 1299--1334. doi:10.3150/15-BEJ779. https://projecteuclid.org/euclid.bj/1486177400