A note on limit theorems for perturbed empirical processes
type: Item
instance of: scholarly article
title: A note on limit theorems for perturbed empirical processes
zbMATH Open document ID: 0684.60005
DOI: 10.1016/0304-4149(89)90073-2
published in: Stochastic Processes and their Applications
publication date: 1989-01-01T00:00:00Z
review text: Dans cet article l'auteur montre un théorème de loi forte des grands nombres, uniforme sur les classes des fonctions, pour le processus empirique perturbé. On definit ce processus comme \(Z_ n(f)=\int f(x)d(P_ n*\mu_ n)\) (où \(P_ n\) est la mesure empirique et \(\mu_ n\) converge en loi vers \(\delta_ 0)\). Il considère dans un premier temps des conditions nécessaires et suffisantes pour qu'il y ait convergence presque sure, ensuite il applique ce théorème à differentes classes de fonctions, en particulier pour les indicatrices des démi-spaces dans \({\mathbb{R}}^ k\). Ensuite il trouve des conditions d'entropie avec crochets pour qu'un principe d'invariance faible soit verifié.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 4121113
zbMATH Keywords: laws of large numbers
zbMATH Keywords: invariance principles
zbMATH Keywords: perturbed empirical distribution functions
author: J. E. Yukich
reviewed by: José R. León
MaRDI profile type: Publication
full work available at URL: 0304-4149(89)90073-2
OpenAlex ID: W2017445417
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description: scientific article; zbMATH DE number 4121113