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A Survey of Multidimensional Medians

Christopher G. Small
International Statistical Review / Revue Internationale de Statistique
Vol. 58, No. 3 (Dec., 1990), pp. 263-277
DOI: 10.2307/1403809
Stable URL: http://www.jstor.org/stable/1403809
Page Count: 15
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A Survey of Multidimensional Medians
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Abstract

In this paper we survey a sequence of papers whose primary aim is the generalization of the concept of the median into higher dimensional settings. While a variety of distinct definitions of the median of a multivariate data set are possible these definitions have the common property of producing the usual definition when applied to univariate data or a univariate distribution. Some common ideas of equivariance, symmetry and breakdown are discussed as well as computational convenience for each definition. The extension of these ideas to directional statistics is also discussed. /// L'auteur revoit une série d'articles qui généralisent de plusieurs manières le concept de médiane dans les espaces multidimensionnels. Ces différentes mesures reproduisent la definition usuelle de la médiane dans le cas de loi unidimensionnelle. Il examine en outre les concepts d'équivariance, de symmétrie, de rupture ainsi que la difficulté de calcul de la médiane pour chaque definition. Enfin, il généralise ces idées pour les lois directionnelles.

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