IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i12p3242-3248.html
   My bibliography  Save this article

An evolutionary algorithm for robust regression

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00162-3
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nunkesser, Robin & Morell, Oliver, 2008. "Evolutionary algorithms for robust methods," Technical Reports 2008,29, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Nguyen, T.D. & Welsch, R., 2010. "Outlier detection and least trimmed squares approximation using semi-definite programming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3212-3226, December.
    3. Hawkins, Douglas M. & Olive, David, 1999. "Applications and algorithms for least trimmed sum of absolute deviations regression," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 119-134, December.
    4. Schyns, M. & Haesbroeck, G. & Critchley, F., 2010. "RelaxMCD: Smooth optimisation for the Minimum Covariance Determinant estimator," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 843-857, April.
    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. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1500-1529, December.
    7. Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "Models where the Least Trimmed Squares and Least Median of Squares estimators are maximum likelihood," CREATES Research Papers 2019-15, Department of Economics and Business Economics, Aarhus University.
    8. Roelant, E. & Van Aelst, S. & Croux, C., 2009. "Multivariate generalized S-estimators," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 876-887, May.
    9. Selin Ahipaşaoğlu, 2015. "Fast algorithms for the minimum volume estimator," Journal of Global Optimization, Springer, vol. 62(2), pages 351-370, June.
    10. 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.
    11. Olive, David J., 2004. "A resistant estimator of multivariate location and dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 93-102, May.
    12. Flores, Salvador, 2010. "On the efficient computation of robust regression estimators," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3044-3056, December.
    13. Kudraszow, Nadia L. & Maronna, Ricardo A., 2011. "Estimates of MM type for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1280-1292, October.
    14. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
    15. Hawkins, Douglas M., 1995. "Convergence of the feasible solution algorithm for least median of squares regression," Computational Statistics & Data Analysis, Elsevier, vol. 19(5), pages 519-538, May.
    16. Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.
    17. Bernholt, Thorsten & Nunkesser, Robin & Schettlinger, Karen, 2007. "Computing the least quartile difference estimator in the plane," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 763-772, October.
    18. Cizek, P., 2004. "Asymptotics of Least Trimmed Squares Regression," Other publications TiSEM dab5d551-aca6-40bf-b92e-c, Tilburg University, School of Economics and Management.
    19. Sirkiä, Seija & Taskinen, Sara & Oja, Hannu, 2007. "Symmetrised M-estimators of multivariate scatter," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1611-1629, September.
    20. Ian L. Dryden & Gary Walker, 1999. "Highly Resistant Regression and Object Matching," Biometrics, The International Biometric Society, vol. 55(3), pages 820-825, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3242-3248. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.