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The fast-tau estimator for regression

Matias Salibian-Barrera, Gert Willems (UGent) and Ruben Zamar
(2008) JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS. 17(3). p.659-682
Author
Organization
Abstract
Yohai and Zamar's (1988) tau-estimators of regression have excellent statistical properties but are nevertheless rarely used in practice due to their lack of software implementation and the general impression that tau-estimators are difficult to approximate. We will show, however, that the computational difficulties we must overcome to approximate tau-estimators are similar in nature to those of the more popular S-estimators. In particular, we implement an approximating algorithm based on random resampling. The main goal of this paper is to compare this random resampling approach with some alternative heuristic search algorithms. We show that the former is not only simpler, but that when enhanced by local improvement steps it generally outperforms the considered heuristic search algorithms, even when these heuristic algorithms also incorporate local improvement steps. Additionally, we show that the random resampling algorithm for approximating tau-estimators has favourable statistical properties compared to the analogous and widely used algorithms for S- and least trimmed squares estimators.
Keywords
simulated annealing, Robust regression, random resampling, tau-estimators, tabu search

Citation

Please use this url to cite or link to this publication:

MLA
Salibian-Barrera, Matias, et al. “The Fast-Tau Estimator for Regression.” JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, vol. 17, no. 3, 2008, pp. 659–82, doi:10.1198/106186008X343785.
APA
Salibian-Barrera, M., Willems, G., & Zamar, R. (2008). The fast-tau estimator for regression. JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, 17(3), 659–682. https://doi.org/10.1198/106186008X343785
Chicago author-date
Salibian-Barrera, Matias, Gert Willems, and Ruben Zamar. 2008. “The Fast-Tau Estimator for Regression.” JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 17 (3): 659–82. https://doi.org/10.1198/106186008X343785.
Chicago author-date (all authors)
Salibian-Barrera, Matias, Gert Willems, and Ruben Zamar. 2008. “The Fast-Tau Estimator for Regression.” JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 17 (3): 659–682. doi:10.1198/106186008X343785.
Vancouver
1.
Salibian-Barrera M, Willems G, Zamar R. The fast-tau estimator for regression. JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS. 2008;17(3):659–82.
IEEE
[1]
M. Salibian-Barrera, G. Willems, and R. Zamar, “The fast-tau estimator for regression,” JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, vol. 17, no. 3, pp. 659–682, 2008.
@article{715129,
  abstract     = {{Yohai and Zamar's (1988) tau-estimators of regression have excellent statistical properties but are nevertheless rarely used in practice due to their lack of software implementation and the general impression that tau-estimators are difficult to approximate. We will show, however, that the computational difficulties we must overcome to approximate tau-estimators
are similar in nature to those of the more popular S-estimators.  In particular, we implement an approximating algorithm based on random resampling. 
The main goal of this paper is to compare this random resampling approach with some alternative heuristic search algorithms. We show that the former is not only simpler, but that when enhanced by local improvement steps it generally
outperforms the considered heuristic search algorithms, even when these heuristic algorithms also incorporate local improvement steps.  Additionally, we show that the random resampling algorithm for approximating tau-estimators has favourable statistical properties compared to the analogous and widely used algorithms for S- and least trimmed squares
estimators.}},
  author       = {{Salibian-Barrera, Matias and Willems, Gert and Zamar, Ruben}},
  issn         = {{1061-8600}},
  journal      = {{JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS}},
  keywords     = {{simulated annealing,Robust regression,random resampling,tau-estimators,tabu search}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{659--682}},
  title        = {{The fast-tau estimator for regression}},
  url          = {{http://doi.org/10.1198/106186008X343785}},
  volume       = {{17}},
  year         = {{2008}},
}
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