Poisson intensity parameter estimation for stationary Gibbs point processes of finite interaction range

Jean-François Coeurjolly (1) , Nadia Morsli (1)

1 FIGAL - Fiabilité et Géométrie Aléatoire

We introduce a semi-parametric estimator of the Poisson intensity parameter of a spatial stationary Gibbs point process. Under very mild assumptions satisfied by a large class of Gibbs models, we establish its strong consistency and asymptotic normality. We also consider its finite-sample properties in a simulation study.

Mots clés: central limit theorem; Georgii-Nguyen-Zessin formula; Papangelou conditional intensity; semi-parametric estimation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-François Coeurjolly, Nadia Morsli. Poisson intensity parameter estimation for stationary Gibbs point processes of finite interaction range. Spatial Statistics, 2013, 4, pp.45-56. ⟨10.1016/j.spasta.2013.02.003⟩. ⟨hal-00742374v2⟩