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Robust regression using iteratively reweighted least-squares.
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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“The regression fit is shown in Table 6, supporting the notion of a negative relationship between the virtual arm length and the hand movement dispersion.”
From Extending body space in immersive virtual reality: a very long arm illusion (2012) · cites this paper as [27]
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Metadata
- Authors
- Holland, P. W., & Welsch, R. E.
- Affiliations
- Educational Testing Service (US)
- National Bureau of Economic Research (US)
- 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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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