Stein estimation of the intensity of a spatial homogeneous Poisson point process

Marianne Clausel (1) , Jean-François Coeurjolly (2) , Jérôme Lelong (1)

1 DAO - Données, Apprentissage et Optimisation
2 FIGAL - Fiabilité et Géométrie Aléatoire

In this paper, we revisit the original ideas of Stein and propose an estimator of the intensity parameter of a homogeneous Poisson point process defined in R^d and observed in a bounded window. The procedure is based on a new general integration by parts formula for Poisson point processes. We show that our Stein estimator outperforms the maximum likelihood estimator in terms of mean squared error. In particular, we show that in many practical situations we have a gain larger than 30%.

Mots clés: superefficient estimator; Stein formula; spatial point process; intensity estimation; Malliavin calculus

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

Marianne Clausel, Jean-François Coeurjolly, Jérôme Lelong. Stein estimation of the intensity of a spatial homogeneous Poisson point process. The Annals of Applied Probability, 2016, 26 (3), pp.1495-1534. ⟨10.1214/15-AAP1124⟩. ⟨hal-01024648v3⟩