Title: The halfspace depth characterization problem
Authors: Stanislav Nagy - Charles University (Czech Republic) [presenting]
Abstract: The halfspace depth is an inferential tool that aims to generalize quantiles to multivariate datasets. It has been long conjectured that, just as for the usual quantiles, there is a one-to-one relation between all Borel probability measures, and all possible depth surfaces. We answer this conjecture in the negative. That suggests an interesting open problem of characterizing those probability measures that possess a unique depth. A complete solution to this problem would have far-reaching implications, not only in the theory of multivariate statistics.