Bahadur representations for robust scale estimators based on regression residuals
type: Item
instance of: scholarly article
title: Bahadur representations for robust scale estimators based on regression residuals
zbMATH Open document ID: 0604.62028
author: Alan H. Welsh
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: Let \(\theta_ n\) be an initial estimate in the regression model \(y_ j=x_ j'\theta +e_ j\) and denote by \(e_ j(\theta_ n)\) the residuals \(y_ j-x_ j'\theta_ n\). The paper derives asymptotic Bahadur representations for the interquartile range and the median absolute deviation of the \(e_ j(\theta_ n)'s\) under weak conditions on the design and the distribution of the \(e_ j's\). These representations are the same as for known \(\theta\). As a corollary the asymptotic behaviour of these two scale estimates follows and their use as concomitant scale estimates in robust regression M-estimators is justified.
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 3976094
zbMATH Keywords: residuals
zbMATH Keywords: asymptotic Bahadur representations
zbMATH Keywords: interquartile range
zbMATH Keywords: median absolute deviation
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: scale estimates
zbMATH Keywords: robust regression M-estimators
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350064
OpenAlex ID: W2044748140
DOI: 10.1214/AOS/1176350064
description: scientific article; zbMATH DE number 3976094