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

Nadia Morsli (1)

1 FIGAL - Fiabilité et Géométrie Aléatoire

We prouve the asymptotic normality of non parametric estimator of pairwise interaction function for stationary pairwise interaction point process characterized by the Papangelou conditional intensity, and obseved on in a bounded window $\Lambda_n$ where ($\Lambda_n )_{n\geq 1}$ is a sequence of cubes growing up to $\R^d$. The proof is based on the m-approximation method in the setting of dependent random fields indexed by $\Z^d$ where $d$ is a positive integer.

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

Domaines: Statistiques [math.ST]

Nadia Morsli. On asymptotic normality of nonparametric estimate for stationary pairwise interaction point process. 2015. ⟨hal-01121114v1⟩