Donsker classes and random geometry
type: Item
instance of: scholarly article
title: Donsker classes and random geometry
zbMATH Open document ID: 0637.60040
author: Michel Talagrand
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: Let \({\mathcal F}\) be a class of square integrable functions. The empirical process indexed by \({\mathcal F}\) is investigated. The paper presents a refinement of the results of \textit{E. Giné} and \textit{J. Zinn}, Ann. Probab. 12, 929-989 (1984; Zbl 0553.60037), concerning the CLT under random entropy conditions. Necessary and sufficient conditions are found. They mean that the trace of \({\mathcal F}\) on a random sample is a small (for the \(\ell^ 1\) norm) perturbation of a set which is nice for the \(\ell^ 2\) norm.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4038916
zbMATH Keywords: central limit theorems
zbMATH Keywords: empirical processes
zbMATH Keywords: functional Donsker classes
reviewed by: G. T. Symm
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991979
OpenAlex ID: W2087372136
DOI: 10.1214/AOP/1176991979
description: scientific article; zbMATH DE number 4038916