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

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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


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