Computational Statistics

, Volume 27, Issue 3, pp 393–410 | Cite as

A comparison of algorithms for the multivariate L 1-median

  • Heinrich FritzEmail author
  • Peter Filzmoser
  • Christophe Croux
Original Paper


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.


Algorithm Multivariate median Optimization Robustness 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Heinrich Fritz
    • 1
    Email author
  • Peter Filzmoser
    • 1
  • Christophe Croux
    • 2
    • 3
  1. 1.Department of Statistics and Probability TheoryVienna University of TechnologyViennaAustria
  2. 2.Faculty of Business and EconomicsK. U. Leuven UniversityLeuvenBelgium
  3. 3.Faculty of Business and EconomicsTilburg UniversityTilburgThe Netherlands

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