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Multivariate permutation tests for the k-sample problem with clustered data

Author

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  • Jörg Rahnenführer

    (Heinrich-Heine-Universität Düsseldorf)

Abstract

Summary We investigate the optimal choice of clustering algorithms for multivariate data sets. We make use of algorithms that define partitions by maximal support planes (MSP) of a convex function and have been profoundly investigated by Pötzelberger and Strasser (2000). This is a wide range class containing as special cases both the well known k-means algorithm and the Kohonen (1985) algorithm. We compare the quality of the clustering procedures by first applying them to multivariate data sets and then treating a k-sample problem. For computing the test statistics the data points are replaced by their conditional expectations with respect to the MSP-partition. Monte Carlo simulations of power functions for tests that are carried out as multivariate permutation tests show a vital and decisive connection between the optimal choice of the algorithm and the tails of the probability distribution of the data. Especially for distributions with heavy tails the performance of k-means type algorithms totally breaks down.

Suggested Citation

  • Jörg Rahnenführer, 2002. "Multivariate permutation tests for the k-sample problem with clustered data," Computational Statistics, Springer, vol. 17(2), pages 165-184, July.
  • Handle: RePEc:spr:compst:v:17:y:2002:i:2:d:10.1007_s001800200100
    DOI: 10.1007/s001800200100
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