Depth of hyperplanes

Abstract

So far, notions of data depths have been discussed that measure how deep a single point is located in a distribution. In many applications, particularly two-sample problems, a statistic is needed that measures how deep a set of points is located in a distribution. For this, the notion of data depth of a set or, more precisely, a data matrix has to be developed. Like in the case of point data depth, many notions are possible and, depending on the application, useful.