Maximum pseudolikelihood estimator for exponential family models of marked Gibbs point processes

TL;DR

This paper develops and analyzes a maximum pseudolikelihood estimator for exponential family Gibbs point processes, proving its strong consistency and asymptotic normality based on a single observed realization.

Contribution

It introduces a new estimator for Gibbs point processes, providing theoretical guarantees under broad conditions and verifying them across various models.

Findings

Estimator is strongly consistent

Estimator is asymptotically normal

Conditions verified on multiple examples

Abstract

This paper is devoted to the estimation of a vector $\bm {\theta}$ parametrizing an energy function of a Gibbs point process, via the maximum pseudolikelihood method. Strong consistency and asymptotic normality results of this estimator depending on a single realization are presented. In the framework of exponential family models, sufficient conditions are expressed in terms of the local energy function and are verified on a wide variety of examples.