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An evolutionary algorithm for robust regression

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  • Nunkesser, Robin
  • Morell, Oliver

Abstract

A drawback of robust statistical techniques is the increased computational effort often needed as compared to non-robust methods. Particularly, robust estimators possessing the exact fit property are NP-hard to compute. This means that--under the widely believed assumption that the computational complexity classes NP and P are not equal--there is no hope to compute exact solutions for large high dimensional data sets. To tackle this problem, search heuristics are used to compute NP-hard estimators in high dimensions. A new evolutionary algorithm that is applicable to different robust estimators is presented. Further, variants of this evolutionary algorithm for selected estimators--most prominently least trimmed squares and least median of squares--are introduced and shown to outperform existing popular search heuristics in difficult data situations. The results increase the applicability of robust methods and underline the usefulness of evolutionary algorithms for computational statistics.

Suggested Citation

  • Nunkesser, Robin & Morell, Oliver, 2010. "An evolutionary algorithm for robust regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3242-3248, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3242-3248
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    References listed on IDEAS

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    1. Nunkesser, Robin, 2008. "RFreak-An R-package for evolutionary computation," Technical Reports 2008,12, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Hawkins, Douglas M., 1993. "The feasible set algorithm for least median of squares regression," Computational Statistics & Data Analysis, Elsevier, vol. 16(1), pages 81-101, June.
    3. Todorov, Valentin, 1992. "Computing the minimum covariance determinant estimator (MCD) by simulated annealing," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 515-525, November.
    4. Hossjer, O. & Croux, C. & Rousseeuw, P. J., 1994. "Asymptotics of Generalized S-Estimators," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 148-177, October.
    5. Agullo, Jose, 2001. "New algorithms for computing the least trimmed squares regression estimator," Computational Statistics & Data Analysis, Elsevier, vol. 36(4), pages 425-439, June.
    6. Hawkins, Douglas M. & Olive, David J., 1999. "Improved feasible solution algorithms for high breakdown estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 1-11, March.
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    Cited by:

    1. Torti, Francesca & Perrotta, Domenico & Atkinson, Anthony C. & Riani, Marco, 2012. "Benchmark testing of algorithms for very robust regression: FS, LMS and LTS," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2501-2512.

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