### Abstract

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 language | English |
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Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 23 |

Volume | 2010-106 |

Publication status | Published - 2010 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2010-106 |

### Keywords

- Algorithm
- Multivariate median
- Optimization
- Robustness

## Cite this

Fritz, H., Filzmoser, P., & Croux, C. (2010).

*A Comparison of Algorithms for the Multivariate L1-Median*. (CentER Discussion Paper; Vol. 2010-106). Econometrics.