Weak and Strong Consistency of non-parametric estimate of potential function for stationary and isotropic pairwise interaction point process

Nadia Morsli (1)

1 FIGAL - Fiabilité et Géométrie Aléatoire

A method is proposed for estimating the potential function of a non-parametric estimator for stationary and isotropic pairwise interaction point process. The relation between a pair potential and the corresponding Papangelou conditional intensity is considered. Consistency and strong consistency of non-parametric estimate are proved in case of finite-range interaction potential.

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

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

Nadia Morsli. Weak and Strong Consistency of non-parametric estimate of potential function for stationary and isotropic pairwise interaction point process. 2015. ⟨hal-01158990v1⟩