- Statist. Surv.
- Volume 13 (2019), 52-118.
Halfspace depth and floating body
Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine geometry are discussed. Maximum halfspace depth may be regarded as a measure of symmetry for random vectors. As such, the maximum depth stands as a generalization of a measure of symmetry for convex sets, well studied in geometry. Under a mild assumption, the upper level sets of the halfspace depth coincide with the convex floating bodies of measures used in the definition of the affine surface area for convex bodies in Euclidean spaces. These connections enable us to partially resolve some persistent open problems regarding theoretical properties of the depth.
Statist. Surv., Volume 13 (2019), 52-118.
Received: September 2018
First available in Project Euclid: 22 June 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H05: Characterization and structure theory 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45] 62G35: Robustness 62H11: Directional data; spatial statistics 62H99: None of the above, but in this section
Nagy, Stanislav; Schütt, Carsten; Werner, Elisabeth M. Halfspace depth and floating body. Statist. Surv. 13 (2019), 52--118. doi:10.1214/19-SS123. https://projecteuclid.org/euclid.ssu/1561169006