Comparison theorems, random geometry and some limit theorems for empirical processes
type: Item
instance of: scholarly article
title: Comparison theorems, random geometry and some limit theorems for empirical processes
zbMATH Open document ID: 0679.60048
author: Michel Talagrand
author: Michel Ledoux
published in: The Annals of Probability
publication date: 1989-01-01T00:00:00Z
review text: A new comparison theorem for Rademacher averages is obtained and by this result the law of the iterated logarithm and the law of large numbers for empirical processes indexed by a family of square integrable functions are proved. The conditions for fulfilling of these laws are quite analogous to the classical conditions of Kolmogorov and Prokhorov. The characterization of the law of the iterated logarithm for empirical processes under some random geometric conditions is also obtained.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4113665
zbMATH Keywords: comparison theorem
zbMATH Keywords: Rademacher averages
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: law of large numbers
zbMATH Keywords: empirical processes
reviewed by: Igor S. Borisov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991418
OpenAlex ID: W1981592894
DOI: 10.1214/AOP/1176991418
description: scientific article; zbMATH DE number 4113665