A Survey of Multidimensional Medians

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.