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...

It has been commonly admitted that the meaning of a descriptive feature of distributions is given by an ordering and that the measures for this feature are meaningful only if they preserve the ordering. However, while many multivariate kurtosis measures have been introduced, multivariate...

Let A1, A2, ..., An and B1, B2, ..., BN be two sequences of events. Let mn(A) and mN(B) be the number of those Aj and Bk, respectively, which occur. Set Sk,t for the joint (k, t)th binomial moment of the vector (mn(A),mN(B)). We prove that linear bounds in terms of the Sk,t on the distribution...