NEW KOLMOGOROV BOUNDS FOR FUNCTIONALS OF BINOMIAL POINT PROCESSES

Abstract : We obtain explicit Berry-Esseen bounds in the Kolmogorov distance 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 recently obtained by Chatterjee (2008), concerning normal approximations in the Wasser-stein 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 covering processes.
Type de document :
Pré-publication, Document de travail
MAP5 2015-19. 2015
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-01155629
Contributeur : Raphael Lachieze-Rey <>
Soumis le : mercredi 27 mai 2015 - 09:29:14
Dernière modification le : mardi 11 octobre 2016 - 12:03:02
Document(s) archivé(s) le : lundi 24 avril 2017 - 15:20:52

Fichier

LRP_Kol_FINAL_2.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01155629, version 1
  • ARXIV : 1505.04640

Collections

Citation

Raphaël Lachièze-Rey, Giovanni Peccati. NEW KOLMOGOROV BOUNDS FOR FUNCTIONALS OF BINOMIAL POINT PROCESSES. MAP5 2015-19. 2015. <hal-01155629>

Partager

Métriques

Consultations de
la notice

139

Téléchargements du document

43