The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Least Median of Squares Regression
Abstract
Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of nearly 50% of contamination in the data. In the special case of simple regression, it corresponds to finding the narrowest strip covering half of the observations. Generalizations are possible to multivariate location, orthogonal regression, and hypothesis testing in linear models.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Huber, P. J. (1981) · Wiley Series in Probability and Statistics · doi:10.1002/0471725250 · Cited by 7,066
Cited by
Gaussian Processes for Machine Learning
Rasmussen, C. E., & Williams, C. K. I. (2005) · doi:10.7551/mitpress/3206.001.0001 · Cited by 11,705
High Breakdown-Point and High Efficiency Robust Estimates for Regression
Yohai, V. J. (1987) · The Annals of Statistics · doi:10.1214/aos/1176350366 · Cited by 1,644
ROBPCA: A New Approach to Robust Principal Component Analysis
Hubert, M., Rousseeuw, P. J., & Vanden Branden, K. (2005) · Technometrics · doi:10.1198/004017004000000563 · Cited by 1,052
Self-citationA Comparative Evaluation of Unsupervised Anomaly Detection Algorithms for Multivariate Data
Goldstein, M., & Uchida, S. (2016) · PLOS ONE · doi:10.1371/journal.pone.0152173 · Cited by 1,032
Seror, R., Ravaud, P., Bowman, S. J., Baron, G., Tzioufas, A., Theander, E., Gottenberg, J.-E., Bootsma, H., Mariette, X., & Vitali, C. (2010) · Annals of the Rheumatic Diseases · doi:10.1136/ard.2009.110619 · Cited by 965
Metadata
- Authors
- Rousseeuw, P. J.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1984-12
- Volume
- 79
- Issue
- 388
- Pages
- 871-880
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2152701363
- Cited by
- 3,835
- References
- 1
- FWCI
- 12.22
- Type
- journal article
- Language
- en
- Open access
- closed
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 ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Least Median of Squares Regression. https://app.cochat.ai/papers/10.1080/01621459.1984.10477105
- The paper
- Rousseeuw, P. J. (1984). Least Median of Squares Regression. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1984.10477105
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
