Maximum pseudo-likelihood estimator for nearest-neighbours Gibbs point processes

Jean-Michel Billiot (1) , Jean-François Coeurjolly (1) , Rémy Drouilhet (1)

1 LABSAD - Laboratoire de Statistiques et Analyse des Données

This paper is devoted to the estimation of a vector parametrizing an energy function associated to some "Nearest-Neighbours" Gibbs point process, via the pseudo-likelihood method. We present some convergence results concerning this estimator, that is strong consistency and asymptotic normality, when only a single realization is observed. Sufficient conditions are expressed in terms of the local energy function and are verified on some examples.

Mots clés: Gibbs point processes; nearest-neighbours models; Delaunay graph; pseudo-likelihood method; minimum contrast estimators.; minimum contrast estimators

Domaines: Statistiques [math.ST]

Jean-Michel Billiot, Jean-François Coeurjolly, Rémy Drouilhet. Maximum pseudo-likelihood estimator for nearest-neighbours Gibbs point processes. 2006. ⟨hal-00016436⟩