Rates of growth and sample moduli for weighted empirical processes indexed by sets
type: Item
instance of: scholarly article
title: Rates of growth and sample moduli for weighted empirical processes indexed by sets
zbMATH Open document ID: 0596.60029
DOI: 10.1007/BF00318708
author: Kenneth S. Alexander
publication date: 1987-01-01T00:00:00Z
review text: Probability inequalities are obtained for the supremum of a weighted empirical process indexed by a Vapnik-Červonenkis class \({\mathbb{C}}\) of sets. These inequalities are particularly useful under the assumption \[ P(\cup \{C\in {\mathbb{C}}:\quad P(C)<t\})\to 0\quad as\quad t\to 0. \] They are used to obtain almost sure bounds on the rate of growth of the process as the sample size approaches infinity, to find an asymptotic sample modulus for the unweighted empirical process, and to study the ratio \(P_ n/P\) of the empirical measure to the actual measure.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 3960661
zbMATH Keywords: inequalities
zbMATH Keywords: supremum of a weighted empirical process
zbMATH Keywords: Vapnik- Červonenkis class
zbMATH Keywords: law of iterated logarithm
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3960661