Laws of large numbers for classes of functions
type: Item
instance of: scholarly article
title: Laws of large numbers for classes of functions
zbMATH Open document ID: 0573.60028
DOI: 10.1016/0047-259X(85)90083-1
published in: Journal of Multivariate Analysis
publication date: 1985-01-01T00:00:00Z
review text: Glivenko-Cantelli theorems are proved for the sequence of empirical measures corresponding to a sequence of independent and identically distributed random elements in a measurable space when these measures are indexed by classes of complex valued functions. The conditions are expressed in terms of metric entropy. The general results are applied to get uniform rate results for kernel density estimators and for empirical characteristic functions.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 3915315
zbMATH Keywords: Glivenko-Cantelli theorems
zbMATH Keywords: empirical measures
zbMATH Keywords: metric entropy
zbMATH Keywords: kernel density estimators
zbMATH Keywords: empirical characteristic functions
author: J. E. Yukich
MaRDI profile type: Publication
cites work: Limit behaviour of the empirical characteristic function
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cites work: Q3921876
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cites work: A law of the logarithm for kernel density estimators
cites work: Q4021149
description: scientific article; zbMATH DE number 3915315