Date: Friday, 8 December 2023, at 12:30pm (Paris) and 7:30pm (Singapore)

Dual format: ESSEC Paris La Défense (CNIT), Room TBA
and via Zoom, please click here

Statistical depth is a non-parametric tool applicable to multivariate and non-Euclidean data. Its goal is to reasonably generalise quantiles to multivariate and more exotic datasets. The first depth was proposed in statistics in 1975; rigorous investigation of depths started in the 1990s, and still, an abundance of open problems stimulates research in the area. We discuss two seminal depths: (i) the halfspace depth (Tukey, 1975) and (ii) the simplicial depth (Liu, 1988). We unveil surprising links between these depths and well-studied concepts from geometry and discrete mathematics. Using these relations, we partially resolve several open problems; in particular, the 30-year-old characterisation conjecture, asking whether two different distributions can correspond to the same halfspace depth.

Kind regards,
Jeremy Heng, Olga Klopp, Roberto Reno, and Marie Kratz
https://crear.essec.edu/crear-events/working-group-on-risk
and Riada Djebbar (Singapore Actuarial Society - ERM)