Spherical data depth and a multivariate median

Abstract

This article introduces the notion of spherical data depth based on random hyperspheres in $R^d$. This depth measure can be used as an exploratory data-analytic technique in a multivariate data analysis or as the basis for the definition of a multivariate median. The major advantage of using the spherical depth rather than a competitor is that the order of computation grows linearly rather than exponentially in the dimension $d$. In this paper, we formally introduce these ideas and illustrate their use using a real-data example.