Asymptotic behavior of robust estimators of regression and scale parameters with fixed carriers
type: Item
instance of: scholarly article
title: Asymptotic behavior of robust estimators of regression and scale parameters with fixed carriers
zbMATH Open document ID: 0598.62077
author: Mervyn J. Silvapulle
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: For a linear regression model, \(y_ i=x_ i\beta +\epsilon_ i\), where \(x_ i=(1,x_{i2},...,x_{ip})\) are known, the estimates (\({\hat \beta}\),\({\hat \sigma}\)) of the vector of parameters \(\beta\) and the scale of the errors \(\epsilon_ i\), respectively, are considered. The estimates were constructed by minimizing the Huber-Dutter loss function \[ \sum \sigma \rho \{(y_ i-x_ i\beta)/\sigma \}+A_ n\sigma \] where \(\rho\geq 0\) is convex, \(\rho (0)=0\), \(t^{-1}\rho (t)\to k\) as \(| t| \to \infty\) for some k, and \(\{A_ n\}\) is some suitably chosen sequence of constants. The asymptotic normality of (\({\hat \beta}\),\({\hat \sigma}\)) under rather general conditions is proved.
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 3965233
zbMATH Keywords: M-estimators
zbMATH Keywords: HD estimator
zbMATH Keywords: simultaneous scale estimation
zbMATH Keywords: Huber-Dutter loss function
zbMATH Keywords: asymptotic normality
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349750
OpenAlex ID: W2006871581
DOI: 10.1214/AOS/1176349750
description: scientific article; zbMATH DE number 3965233