A Comparison of Algorithms for the Multivariate L1-Median

H. Fritz, P. Filzmoser, C. Croux

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The L1-median is a robust estimator of multivariate location with good statistical properties. Several algorithms for computing the L1- median are available. Problem speci c algorithms can be used, but also general optimization routines. The aim is to compare dierent algorithms with respect to their precision and runtime. This is pos- sible because all considered algorithms have been implemented in a standardized manner in the open source environment R. In most sit- uations, 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.
Original languageEnglish
Place of PublicationTilburg
Number of pages23
Publication statusPublished - 2010

Publication series

NameCentER Discussion Paper


  • Algorithm
  • Multivariate median
  • Optimization
  • Robustness

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