On asymptotic normality of nonparametric estimate for stationary pairwise interaction point process

Nadia Morsli (1)

1 FIGAL - Fiabilité et Géométrie Aléatoire

Pairwise interacting point processes form a very popular and flexible class of models for spatial point patterns in a bounded region. In this class, the interaction between two points is described by pairwise interaction function. We prove the asymptotic normality of nonparametric estimator of pairwise interaction function for stationary pairwise interaction point process characterized by the Papangelou conditional intensity, and observed in a bounded window of a sequence of cubes growing up to $\R^d$. Formula for the variance of the resulting estimator can be obtained using Papangelou conditional intensity of the point process. This is a random function satisfying the counterpart of the Georgii-Nguyen-Zessin formula. The proof of the asymptotic normality of the resulting estimator is based on the $m_n$-approximation method in the setting of dependent random fields indexed by $\Z^d$ where $d$ is a positive integer.

Mots clés: Georgii-Nguyen-Zessin formula; non parametric esti-mation; kernel estimators; pairwise interaction point process; Papangelou conditional intensity; asymp-totic normality; m-dependence

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Nadia Morsli. On asymptotic normality of nonparametric estimate for stationary pairwise interaction point process. 2015. ⟨hal-01121114v2⟩