On the second order efficiency of bootstrap estimators of sampling distributions
type: Item
instance of: scholarly article
title: On the second order efficiency of bootstrap estimators of sampling distributions
zbMATH Open document ID: 0661.62030
author: Takeru Suzuki
published in: Tokyo Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Given \(X_ i\) i.i.d. with d.f. F, let \(g_ n(.,F)\) be the d.f. of an appropriate normalized statistic based on \(X_ 1,...,X_ n\) and let \(\hat g_{n,B}=g_ n(.,\hat F_ n)\) be the bootstrap estimator of \(g_ n(.,F)\), where \(\hat F_ n\) is the empirical d.f. based on \(X_ 1,...,X_ n\). The present paper proves second order asymptotic efficiency in the sense of \textit{M. Akahira} and \textit{K. Takeuchi} [Asymptotic efficiency of statistical estimators: concepts and higher order asymptotic efficiency. (1981; Zbl 0463.62026)], of an appropriately corrected version of \(\hat g_{n,B}\) under conditions about \(g_ n(.,F)\) similar to Ass. 1 or 1' of \textit{R. Beran} [Ann. Stat. 10, 212-225 (1982; Zbl 0485.62037)].
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G15
zbMATH DE Number: 4080633
zbMATH Keywords: bootstrap estimator
zbMATH Keywords: second order asymptotic efficiency
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270134271
OpenAlex ID: W2088368268
DOI: 10.3836/TJM/1270134271
description: scientific article; zbMATH DE number 4080633