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

Abstract

This paper is devoted to the estimation of a vector θ 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.