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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Robust regression supports a negative relationship between virtual arm length and hand movement dispersion.
“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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Sun, W., Shao, Q., & Liu, J. (2013) · Journal of Geographical Sciences · doi:10.1007/s11442-013-1065-z · Cited by 182 · see citing works
Real-Time Regularized Ultrasound Elastography
Rivaz, H. J., Boctor, E. M., Choti, M. A., & Hager, G. D. (2010) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2010.2091966 · Cited by 181 · see citing works
Pixel-Perfect Structure-from-Motion with Featuremetric Refinement
Lindenberger, P., Sarlin, P.-E., Larsson, V., & Pollefeys, M. (2021) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv48922.2021.00593 · Cited by 181 · see citing works
Benchmarking regression algorithms for loss given default modeling
Loterman, G., Brown, I., Martens, D., Mues, C., & Baesens, B. (2011) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2011.01.006 · Cited by 180 · see citing works
Kellman, P., Arai, A. E., & Xue, H. (2013) · Journal of Cardiovascular Magnetic Resonance · doi:10.1186/1532-429x-15-56 · Cited by 178 · see citing works
Separating physiologically and directionally induced changes in PRI using BRDF models
Hilker, T., Coops, N. C., Hall, F. G., Black, T. A., Wulder, M. A., Nesic, Z., & Krishnan, P. (2008) · Remote Sensing of Environment · doi:10.1016/j.rse.2008.01.011 · Cited by 176 · see citing works
Landslide displacement forecasting using deep learning and monitoring data across selected sites
Nava, L., Carraro, E., Reyes‐Carmona, C., Puliero, S., Bhuyan, K., Rosi, A., Monserrat, O., Floris, M., Meena, S. R., Galvé, J. P., et al. (2023) · Landslides · doi:10.1007/s10346-023-02104-9 · Cited by 176 · see citing works
A review on robust M-estimators for regression analysis
de Menezes, D. Q. F., Prata, D. M., Secchi, A. R., & Pinto, J. C. (2021) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2021.107254 · Cited by 175 · see citing works
Statistical Robustness: One View of Its Use in Applications Today
Hogg, R. V. (1979) · The American Statistician · doi:10.1080/00031305.1979.10482673 · Cited by 173 · see citing works
- 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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