Halfspace depth: Geometry of multivariate quantiles
Event details
| Date | 28.10.2022 |
| Hour | 15:15 › 17:00 |
| Speaker | Stanislav Nagy (Charles University) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Statistical depth is a non-parametric tool applicable to multivariate and non-Euclidean data, whose goal is a reasonable generalisation of quantiles to multivariate and more exotic datasets. We discuss the halfspace depth, arguably the most crucial depth in statistics. J. W. Tukey proposed that depth in 1975; its rigorous investigation started in the 1990s, and still, an abundance of open problems stimulates research in the area.
We present surprising links of the halfspace depth with well-studied concepts from convex geometry. Using these relations, we partially resolve several open problems concerning depth. In particular, we resolve the 30-year-old characterisation conjecture, asking whether two different measures can correspond to the same halfspace depth.
Practical information
- Informed public
- Free
Organizer
- Tomas Masak
Contact
- Maroussia Schaffner