Asymptotic normality of the L1-error for Geffroy's estimate of point process boundaries

Stéphane Girard (1) , Pierre Jacob (2)

1 MISTIS [?-2006] - Modelling and Inference of Complex and Structured Stochastic Systems [?-2006]
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

In this Note, the L\- error of Geffroy’s estimate of a Poisson point process boundary is shown to be asymptoticallv normal. We give conditions such that the asymptotic mean and variance do not depend on the unknown boundary. This resuit is illustrated by a simulation.

Mots clés: Extreme values; Poisson process; central limit theorern

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

Stéphane Girard, Pierre Jacob. Asymptotic normality of the L1-error for Geffroy's estimate of point process boundaries. Publications de l'Institut de Statistique de l'Université de Paris, 2005, XLIX, pp.3-17. ⟨hal-00383170⟩