On Newton's method for Huber's robust M-estimation problems in linear regression
type: Item
instance of: scholarly article
title: On Newton's method for Huber's robust M-estimation problems in linear regression
zbMATH Open document ID: 0924.65153
DOI: 10.1007/BF02510408
author: K. Appert
published in: BIT
publication date: 1999-04-27T00:00:00Z
review text: The Newton-type method for computing Huber's robust \(M\)-estimator in the linear regression model of \textit{K. Madsen} and \textit{H. B. Nielsen} [BIT 30, No. 4, 682-699 (1990; Zbl 0717.65118)] is reconsidered. The following enhancements to the original algorithm are studied: \(\bullet\) Finite termination property of the algorithm is proved without any assumption on the \(M\)-estimation problem. \(\bullet\) It is not necessary to make restrictions on the choice of the search direction and the step length in some degenerate cases. Detailed algorithms are given and it is proved that the modified Newton-type algorithm finds a minimizer in a finite number of iterations.
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 1251185
zbMATH Keywords: Huber's \(M\)-estimate
zbMATH Keywords: robust regression
zbMATH Keywords: Newton's method
zbMATH Keywords: finite convergence
zbMATH Keywords: algorithm
zbMATH Keywords: linear regression
reviewed by: Jaromír Antoch
describes a project that uses: AAFAC
MaRDI profile type: Publication
cites work: Q4868581
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full work available at URL: https://doi.org/10.1007/bf02510408
OpenAlex ID: W1993619493
description: scientific article; zbMATH DE number 1251185