Department of
Applied
Mathematics

Halfspace depth and the geometry of multivariate quantiles

Stanislav Nagy

Abstract

Statistical data depth is a non-parametric tool applicable to multivariate data, whose main goal is a reasonable generalisation of quantiles to multivariate datasets. We discuss the halfspace depth, the most important depth in statistics. This depth was first proposed in 1975; its rigorous investigation starts in the 1990s, and still an abundance of open problems stimulates the research in the area. We present several interesting links of the halfspace depth, and some well-studied concepts from geometry. Using these relations we resolve some open problems concerning data depth, and outline perspectives for future research both in data depth, and in convex geometry.

The talk is intended to be largely self-contained; no particular knowledge of probability and statistics is necessary.