Uniform strong consistency of nonparametric estimator for stationary pairwise interaction point processes under mixing conditions

Nadia Morsli (1)

1 FIGAL - Fiabilité et Géométrie Aléatoire

We suggest a new nonparametric estimate of the interaction function of pairwise interaction point process on $\R^d$ such that its Papangelou conditional intensity is translation invariant and satisfied finite-range interaction. We prove uniform strong consistency of the nonparametric estimate of the interaction function . Sufficient conditions of the rates of uniform strong consistency for the resulting kernel-type estimator are valid by the nonuniform mixing condition for a stationary point process, which can be viewed interchangeably as a lattice field in $\Z^d$.

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

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

Nadia Morsli. Uniform strong consistency of nonparametric estimator for stationary pairwise interaction point processes under mixing conditions. 2016. ⟨hal-01179943v2⟩