Parametric estimation of pairwise Gibbs point processes with infinite range interaction

TL;DR

This paper develops new statistical inference methods for infinite range Gibbs point processes, extending classical techniques and proving their consistency and asymptotic normality under certain conditions.

Contribution

It introduces extensions of pseudolikelihood and logistic regression methods to infinite range models and proves their strong consistency and CLT.

Findings

Estimators are strongly consistent.

Establishes a CLT for the estimators.

Applicable to Ruelle superstable and lower regular models.

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 pseudolikelihood 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.