A comparison of algorithms for the multivariate L ^sub 1^-median

The L ^sub 1^-median is a robust estimator of multivariate location with good statistical properties. Several algorithms for computing the L ^sub 1^-median are available. Problem specific algorithms can be used, but also general optimization routines. The aim is to compare different algorithms with...

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Bibliographic Details
Published in:Computational statistics 2012-09, Vol.27 (3), p.393
Main Authors: Fritz, Heinrich, Filzmoser, Peter, Croux, Christophe
Format: Article
Language:English
Subjects:
Algorithms
Methods
Multivariate analysis
Optimization
Principal components analysis
Simplex method
Studies
Online Access:Get full text
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Summary:The L ^sub 1^-median is a robust estimator of multivariate location with good statistical properties. Several algorithms for computing the L ^sub 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.[PUBLICATION ABSTRACT]
ISSN:0943-4062
1613-9658
DOI:10.1007/s00180-011-0262-4