Bootstrapping \(M\)-estimators of a multiple linear regression parameter
type: Item
instance of: scholarly article
title: Bootstrapping \(M\)-estimators of a multiple linear regression parameter
zbMATH Open document ID: 0792.62058
published in: The Annals of Statistics
publication date: 1993-04-01T00:00:00Z
review text: This paper considers a multiple linear regression model \(Y_ i= X_ i' \beta+\varepsilon_ i\), where the errors \(\varepsilon_ i\) are independent random variables with common distribution \(F\) and the \(X_ i\) are known design vectors. Let \(\overline{\beta}_ n\) be the \(M\)- estimator of \(\beta\) corresponding to a score function \(\psi\). Two-term Edgeworth expansions for the distributions of standardized and Studentized \(\overline{\beta}_ n\) are obtained under some conditions on \(F\), \(\psi\) and the design. Also, it is shown that the bootstrap method is second order correct.
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62G09
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 150377
zbMATH Keywords: independent random errors
zbMATH Keywords: Studentized estimators
zbMATH Keywords: two-term Edgeworth expansions
zbMATH Keywords: multiple linear regression model
zbMATH Keywords: \(M\)-estimator
zbMATH Keywords: score function
zbMATH Keywords: bootstrap method
zbMATH Keywords: second order correct
author: Soumendra N. Lahiri
reviewed by: Guijing Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348784
OpenAlex ID: W2089022571
DOI: 10.1214/AOS/1176348784
description: scientific article; zbMATH DE number 150377