In this article, we study a class of projection based scatter depth functions proposed by Zuo [Y. Zuo, Robust location and scatter estimators in multivariate analysis, The Frontiers in Statistics, Imperial College Press, 2005. Invited book chapter to honor Peter Bickel on his 65th Birthday]. In...

Given a multivariate probability distribution F, a corresponding depth function orders points according to their "centrality" in the distribution F. One useful role of depth functions is to generate two-dimensional curves for convenient and practical description of particular features of a...

In this paper, a family of kurtosis orderings for multivariate distributions is proposed and studied. Each ordering characterizes in an affine invariant sense the movement of probability mass from the "shoulders" of a distribution to either the center or the tails or both. All even moments of...