Cited by 2,115Advanced Statistical Methods and ModelsStatistical and numerical algorithmsStatistical Distribution Estimation and Applications

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Robust regression using iteratively reweighted least-squares.

Holland, Paul W., Welsch, Roy E.·1977·Communications in Statistics - Theory and Methods

DOI 10.1080/03610927708827533

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Abstract

The rapid development of the theory of robust estimation (Huber, 1973) has created a need for computational procedures to produce robust estimates. We will review a number of different computational approaches for robust linear regression but focus on one—iteratively reweighted least-squares (IRLS). The weight functions that we discuss are a part of a semi-portable subroutine library called ROSEPACK (RObust Statistical Estimation PACKage) that has been developed by the authors and Virginia Klema at the Computer Research Center of the National Bureau of Economic Research, Inc. in Cambridge, Mass. with the support of the National Science Foundation. This library (Klema, 1976) makes it relatively simple to implement an IRLS regression package.

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Self-citation
Minimization Techniques for Piecewise Differentiable Functions: The $l_1$ Solution to an Overdetermined Linear System
Bartels, R. H., Conn, A. R., & Sinclair, J. W. (1978) · SIAM Journal on Numerical Analysis · doi:10.1137/0715015 · Cited by 149

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Authors: Holland, P. W., & Welsch, R. E.
Affiliations: Educational Testing Service (US)
National Bureau of Economic Research (US)
ORCID: Holland, Paul W.
Welsch, Roy E.
Venue: Communications in Statistics - Theory and Methods
Publisher: Informa UK Limited
Published: 1977-01
Volume: 6
Issue: 9
Pages: 813-827
ISSN: 0361-0926 (ISSN-L)
1532-415X
DOI: 10.1080/03610927708827533
OpenAlex: W2050551672
Cited by: 2,115
References: 18
Citations by year: 2026: 97 · 2025: 112 · 2024: 121 · 2023: 110 · 2022: 123 · 2021: 123 · 2020: 128 · 2019: 103 · 2018: 105 · 2017: 108 · 2016: 104 · 2015: 101 · 2014: 101 · 2013: 61 · 2012: 48
FWCI: 5.33
Type: journal article
Language: en
Open access: closed
Locations: Communication in Statistics- Theory and Methods (publishedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Keywords: robust regression, iteratively reweighted least squares, robust estimation, weight functions, robust linear regression

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Robust regression using iteratively reweighted least-squares.

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