The expected convex hull trimmed regions of a sample

Given a data set in the multivariate Euclidean space, we study regions of central points built by averaging all their subsets with a fixed number of elements. The averaging of these sets is performed by appropriately scaling the Minkowski or elementwise summation of their convex hulls. The volume of such central regions is proposed as a multivariate scatter estimate and a circular sequence algorithm to compute the central regions of a bivariate data set is described. Extended version of the conference paper Cascos (2006) presented at the 17th Conference of the European Regional Section of the International Association for Statistical Computing (COMPSTAT 2006, Rome, Italy, August 28–September 1, 2006). Supported by the Spanish Ministry of Education and Science under grant MTM2005-02254.