The DOI matches its Crossref record; 17 of the 18 references it cites were found in a registry or an index.
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]
Citations
Cites
Robust estimation of a location parameter
Huber, P. J. (1964) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177703732 · Cited by 7,228
Robust Regression: Asymptotics, Conjectures and Monte Carlo
Huber, P. J. (1973) · The Annals of Statistics · doi:10.1214/aos/1176342503 · Cited by 2,337
The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data
Beaton, A. E., & Tukey, J. W. (1974) · Technometrics · doi:10.1080/00401706.1974.10489171 · Cited by 967
A Robust Method for Multiple Linear Regression
Andrews, D. F. (1974) · Technometrics · doi:10.1080/00401706.1974.10489233 · Cited by 639
An Improved Algorithm for Discrete $l_1 $ Linear Approximation
Barrodale, I., & Roberts, F. D. K. (1973) · SIAM Journal on Numerical Analysis · doi:10.1137/0710069 · Cited by 608
Robust Estimates of Location: Survey and Advances.
HINKLEY, D. V., Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H., & Tukey, J. W. (1973) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2345006 · Cited by 534
One-Step Huber Estimates in the Linear Model
Bickel, P. J. (1975) · Journal of the American Statistical Association · doi:10.1080/01621459.1975.10479884 · Cited by 338
Robust Estimates of Location: Survey and Advances
Andrews, D. F., & Hampel, F. R. (2015) · Princeton University Press eBooks · doi:10.1515/9781400867011 · Cited by 292
Techniques for nonlinear least squares and robust regression
Dennis, J. E., & Welsch, R. E. (1978) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610917808812083 · Cited by 165
Self-citationBartels, R. H., Conn, A. R., & Sinclair, J. W. (1978) · SIAM Journal on Numerical Analysis · doi:10.1137/0715015 · Cited by 149
Research works printed but not linked: 5
- Fair R. C., 1974, Ann. Econ. Social Measurement, 3, 667
- Gross A. M., 1977, J. Amer. Statist. Assoc.
- Hill R. W., 1977, J. Amer. Statist. Assoc.
- Klema, V. 1976. Proc. Bicentennial Conf. Math. Program. An iteratively reweighted least squares system. 1976. to appear
- Welsch R. E., 1975, 1975 Proc. Amer. Statist. Assoc. Statist. Comp. Section, 36
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Alexandrov, L. B., Ju, Y. S., Haase, K., Van Loo, P., Martincorena, I., Nik-Zainal, S., Totoki, Y., Fujimoto, A., Nakagawa, H., Shibata, T., et al. (2016) · Science · doi:10.1126/science.aag0299 · Cited by 1,100
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
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