New Berry-Esseen bounds for functionals of binomial point processes - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue The Annals of Applied Probability Année : 2017

New Berry-Esseen bounds for functionals of binomial point processes

Résumé

We obtain explicit Berry-Esseen bounds in the Kolmogorov dis- tance for the normal approximation of non-linear functionals of vectors of independent random variables. Our results are based on the use of Stein’s method and of random difference operators, and generalise the bounds obtained by Chatterjee (2008), concerning normal approximations in the Wasserstein distance. In order to obtain lower bounds for variances, we also revisit the classical Hoeffding decompositions, for which we provide a new proof and a new representation. Several applications are discussed in detail: in particular, new Berry-Esseen bounds are obtained for set approximations with random tessellations, as well as for functionals of coverage processes.
Fichier principal
Vignette du fichier
LRP-Kol-AoAP-finalversion-rlr.pdf (438.83 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01155629 , version 1 (27-05-2015)
hal-01155629 , version 2 (09-11-2017)

Identifiants

Citer

Raphaël Lachièze-Rey, Giovanni Peccati. New Berry-Esseen bounds for functionals of binomial point processes. The Annals of Applied Probability, 2017, 27 (4), pp.1992-2031. ⟨hal-01155629v2⟩
155 Consultations
371 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More