Title: Halfspace depths for scatter, concentration and shape matrices
Authors: Davy Paindaveine - Universite libre de Bruxelles (Belgium) [presenting]
Germain Van Bever - Universite de Namur (Belgium)
Abstract: Halfspace depth concepts for scatter, concentration and shape matrices are proposed. For scatter matrices, our concept extends a previous one to the non-centered case. Rather than focusing, as in earlier works, on deepest scatter matrices, we thoroughly investigate the properties of the proposed depth and of the corresponding depth regions. We do so under minimal assumptions and, in particular, we do not restrict to elliptical distributions nor to absolutely continuous distributions. Interestingly, fully understanding scatter halfspace depth requires considering different geometries/topologies on the space of scatter matrices. We also discuss the structural properties that a scatter depth should satisfy, and investigate whether or not these are met by the proposed depth. As mentioned above, companion concepts of depth for concentration matrices and shape matrices are also proposed and studied. We illustrate the practical relevance of the proposed concepts by considering a real-data example from finance.