Effect of kurtosis on efficiency of some multivariate medians

Jin Wang, Weihua Zhou

Research output: Contribution to journalArticle

Abstract

Up to now, various multivariate medians have been proposed. To support their applications, we study the effect of kurtosis on efficiency of some well-known multivariate medians. Results are established for the coordinatewise median, the spatial median, the Oja median, and their modified versions. Such results provide a basis for choosing among the multivariate medians in practical analyses. The effect of dimension on efficiency of those multivariate medians is also studied. It is found that the result of Brown [(1983), ‘Statistical Uses of the Spatial Median’, Journal of the Royal Statistical Society, Series B, 45, 25–30] for the spatial median and spherically symmetric normal distributions can be extended to some other medians and some non-normal distributions but does not hold in general.

Original languageEnglish (US)
Pages (from-to)331-348
Number of pages18
JournalJournal of Nonparametric Statistics
Volume27
Issue number3
DOIs
StatePublished - Jul 3 2015

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Keywords

  • asymptotic relative efficiency
  • elliptically symmetric distribution
  • multivariate kurtosis
  • multivariate median
  • multivariate sign test

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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