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A comparison of algorithms for the multivariate L 1 -median

Author

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  • Heinrich Fritz

    ()

  • Peter Filzmoser

    ()

  • Christophe Croux

    ()

Abstract

The L 1 -median is a robust estimator of multivariate location with good statistical properties. Several algorithms for computing the L 1 -median are available. Problem specific algorithms can be used, but also general optimization routines. The aim is to compare different algorithms with respect to their precision and runtime. This is possible because all considered algorithms have been implemented in a standardized manner in the open source environment R. In most situations, the algorithm based on the optimization routine NLM (non-linear minimization) clearly outperforms other approaches. Its low computation time makes applications for large and high-dimensional data feasible. Copyright Springer-Verlag 2012

Suggested Citation

  • Heinrich Fritz & Peter Filzmoser & Christophe Croux, 2012. "A comparison of algorithms for the multivariate L 1 -median," Computational Statistics, Springer, vol. 27(3), pages 393-410, September.
  • Handle: RePEc:spr:compst:v:27:y:2012:i:3:p:393-410
    DOI: 10.1007/s00180-011-0262-4
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    References listed on IDEAS

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    1. Debruyne, Michiel & Hubert, Mia & Van Horebeek, Johan, 2010. "Detecting influential observations in Kernel PCA," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3007-3019, December.
    2. Daniel Gervini, 2008. "Robust functional estimation using the median and spherical principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 587-600.
    3. 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.
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