On some representations of the bootstrap
type: Item
instance of: scholarly article
title: On some representations of the bootstrap
zbMATH Open document ID: 0658.62047
DOI: 10.1007/BF00339995
author: S. H. Lo
publication date: 1989-01-01T00:00:00Z
review text: The bootstrap statistic \({\hat \theta}{}^*_ n-{\hat \theta}_ n\) is represented as the sum of two terms, one of which has the same distribution as \({\hat \theta}{}_ n-\theta\) and the other is a relatively negligible remainder. The representation is then applied to the problems of estimating a distribution and a quantile. The study includes the tail part of the distribution and quantiles for which the convergence rates could be faster than the usual ``\(n^{-1/2}\)'' rate.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4076333
zbMATH Keywords: bootstrap statistic
zbMATH Keywords: relatively negligible remainder
zbMATH Keywords: quantiles
zbMATH Keywords: convergence rates
zbMATH Keywords: represenation
zbMATH Keywords: uniform distribution
MaRDI profile type: Publication
cites work: Estimated sampling distributions: The bootstrap and competitors
cites work: Some representations of the nonparametric maximum likelihood estimators with truncated data
cites work: Bootstrap methods: another look at the jackknife
cites work: On the asymptotic accuracy of Efron's bootstrap
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full work available at URL: https://doi.org/10.1007/bf00339995
OpenAlex ID: W1993373707
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4076333