Consistency and strong consistency of non-parametric estimate of the potential function of stationary and isotropic pairwise interaction point processes

Nadia Morsli (1)

1 FIGAL - Fiabilité et Géométrie Aléatoire

The paper deals with the Gibbs point processes, which are usually used to model interaction between particles. These processes are defined and characterized through the Papangelou conditional intensity. In the paper, we assume that the model is a stationary pairwise interaction point process, so that its Papangelou conditional intensity involves two terms: a Poisson intensity parameter and a potential function. We suggest a new non-parametric estimator for the potential function in the Papangelou conditional intensity. Consistency and strong consistency for the resulting estimator of the total Papangelou conditional intensity are proved in the case of the finite-range interaction potential.

Mots clés: Papangelou conditional intensity; consistency; rates of strong uniform consistency; Non parametric estimation; kernel-type estimator; pairwise interaction point process

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

Nadia Morsli. Consistency and strong consistency of non-parametric estimate of the potential function of stationary and isotropic pairwise interaction point processes. 2016. ⟨hal-01158990v2⟩