A nonparametric estimator for stationary pairwise interaction point processes under mixing conditions

Nadia Morsli (1)

1 FIGAL - Fiabilité et Géométrie Aléatoire

We consider a nonparametric estimator of the interaction function of pairwise interaction point process such that its Papangelou conditional intensity is translation invariant and satisfied finite-range interaction. This method of nonparametric inference is based on a single observation in a window which is assumed its volume grows unboundedly in all directions as n tends infinity. We prove uniform strong consistency of multivariate nonparametric estimates. The main problem consists in deriving appropriate for uniform strong mixing and strong mixing random fields in Z d under Dobrushin's uniqueness condition.

Mots clés: kernel-type estimator; edge effects; pairwise interaction point process; mixing random fields; rates of converge; Dobrushin uniqueness con-ditions

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

Nadia Morsli. A nonparametric estimator for stationary pairwise interaction point processes under mixing conditions. 2015. ⟨hal-01179943v1⟩