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Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals
Open accessAbstract
An appealing approach to the problem of estimating the regression coefficients in a linear model is to find those values of the coefficients which make the residuals as small as possible. We give some measures of the dispersion of a set of numbers, and define our estimates as those values of the parameters which minimize the dispersion of the residuals. We consider dispersion measures which are certain linear combinations of the ordered residuals. We show that the estimates derived from them are asymptotically equivalent to estimates recently proposed by Jureckova. In the case of a single parameter, we show that our estimate is a "weighted median" of the pairwise slopes $(Y_j - Y_i)/(c^j - c^i)$.
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Cited by
Robust regression methods for computer vision: A review
Meer, P., Mintz, D., Rosenfeld, A., & Kim, D. Y. (1991) · International Journal of Computer Vision · doi:10.1007/bf00127126 · Cited by 638
Covariance Adjustment in Randomized Experiments and Observational Studies
Rosenbaum, P. R. (2002) · Statistical Science · doi:10.1214/ss/1042727942 · Cited by 477
Rfit: Rank-based Estimation for Linear Models
Kloke, J., & McKean, J. (2012) · The R Journal · doi:10.32614/rj-2012-014 · Cited by 267
Chubukov, V., Uhr, M., Le Chat, L., Kleijn, R. J., Jules, M., Link, H., Aymerich, S., Stelling, J., & Sauer, U. (2013) · Molecular Systems Biology · doi:10.1038/msb.2013.66 · Cited by 191
Metadata
- Authors
- Jaeckel, L. A.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1972-10
- Volume
- 43
- Issue
- 5
- Pages
- 1449-1458
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2030296667
- Cited by
- 564
- References
- 0
- FWCI
- 3.25
- Type
- journal article
- Language
- en
- Open access
- diamond
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- CoChat. (2026). Citation check: Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals. https://app.cochat.ai/papers/10.1214/aoms/1177692377
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- Jaeckel, L. A. (1972). Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals. The Annals of Mathematical Statistics. https://doi.org/10.1214/aoms/1177692377
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