A Fast Algorithm for S-Regression Estimates

Equivariant high-breakdown point regression estimates are computationally expensive, and the corresponding algorithms become unfeasible for moderately large number of regressors. One important advance to improve the computational speed of one such estimator is the fast-LTS algorithm. This article pr...

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Bibliographic Details
Published inJournal of computational and graphical statistics Vol. 15; no. 2; pp. 414 - 427
Main Authors Salibian-Barrera, Matías, Yohai, Víctor J
Format Journal Article
LanguageEnglish
Published Alexandria Taylor & Francis 01.06.2006
American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
Taylor & Francis Ltd
Subjects
Algorithms
Datasets
Estimators
High breakdown point
Linear regression
Local minimum
Mathematical robustness
Objective functions
Outliers
Point estimators
Regression analysis
Robustness
Simulation
Studies
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Summary:Equivariant high-breakdown point regression estimates are computationally expensive, and the corresponding algorithms become unfeasible for moderately large number of regressors. One important advance to improve the computational speed of one such estimator is the fast-LTS algorithm. This article proposes an analogous algorithm for computing S-estimates. The new algorithm, that we call "fast-S", is also based on a "local improvement" step of the resampling initial candidates. This allows for a substantial reduction of the number of candidates required to obtain a good approximation to the optimal solution. We performed a simulation study which shows that S-estimators computed with the fast-S algorithm compare favorably to the LTS-estimators computed with the fast-LTS algorithm.
ISSN:1061-8600
1537-2715
DOI:10.1198/106186006X113629