Rates of convergence for the distance between distribution function estimators
type: Item
instance of: scholarly article
title: Rates of convergence for the distance between distribution function estimators
zbMATH Open document ID: 0604.62030
DOI: 10.1007/BF01894748
published in: Metrika
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176051
review text: The content of the paper is accurately given in the author's summary: ''The normed difference between ''kernel'' distribution function estimators \(\hat F{}_ n\) and the empirical distribution function \(F_ n\) is investigated. Conditions on the kernel and bandwidth of \(\hat F{}_ n\) are given so that \(a_ n\| \hat F_ n-F_ n\| \to 0\) with probability 1 as \(n\to \infty\) for both the sup-norm \(\| g\|_{\infty}=\sup | g(x)|\) and \(L_ 1\) norm \(\| g\|_ 1=\int | g(x)| dx\). Applications include equivalence in asymptotic distribution of \(T(\hat F_ n)\) and \(T(F_ n)\) (to order \(a_ n)\) for certain robust functionals T(.).''
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 3976096
zbMATH Keywords: rates of convergence
zbMATH Keywords: kernel density estimators
zbMATH Keywords: weak convergence
zbMATH Keywords: empirical distribution function
zbMATH Keywords: bandwidth
zbMATH Keywords: sup-norm
author: Dennis D. Boos
reviewed by: Aldo J. Viollaz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3976096