Efficiency and robustness in resampling
type: Item
instance of: scholarly article
title: Efficiency and robustness in resampling
zbMATH Open document ID: 0755.62038
author: Regina Y. Liu
author: Kesar Singh
published in: The Annals of Statistics
publication date: 1992-09-27T00:00:00Z
review text: The goal of this paper is to provide a unified framework for classifying different jackknife and bootstrap procedures for linear regression models into two types, type \(E\) (the efficient ones) and type \(R\) (the robust ones). After an introductory first section, section 2 addresses the simple linear regression model \(Y_ i=x_ i\beta+\varepsilon_ i\) with independent errors \(\varepsilon_ i\approx (0,\sigma^ 2_ 1)\) where least squares estimation of \(\beta\) is of interest. It is shown that the resampling variances of the regression estimators satisfy exactly one of two possible representations. This depends mainly on \(\sum x^ 2_ i\). The two representations characterize the efficient and robust groups. Section 3 extends the result to general linear regression. The case of the classical bootstrap in the \(E\)-type and the external bootstrap in the \(R\)-type are presented in detail, other resampling procedures are outlined.
Mathematics Subject Classification ID: 62G09
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 61844
zbMATH Keywords: asymptotic variance
zbMATH Keywords: jackknife procedures
zbMATH Keywords: asymptotic relative efficiency
zbMATH Keywords: E-type resampling procedures
zbMATH Keywords: R-type resampling procedures
zbMATH Keywords: efficient procedures
zbMATH Keywords: robust procedures
zbMATH Keywords: unified framework
zbMATH Keywords: bootstrap procedures
zbMATH Keywords: least squares estimation
zbMATH Keywords: resampling variances
reviewed by: Rainer Schlittgen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348527
OpenAlex ID: W2088473244
DOI: 10.1214/AOS/1176348527
description: scientific article; zbMATH DE number 61844