Halfspace depth and floating body

DOI10.1214/19-SS123zbMath1428.62204arXiv1809.10925WikidataQ115907981 ScholiaQ115907981MaRDI QIDQ2002525

Elisabeth M. Werner, Stanislav Nagy, Carsten Schuett

Publication date: 12 July 2019

Published in: Statistics Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.10925

zbMATH Keywords

designhalfspace depthfloating bodyTukey depthstatistical depthmeasures of symmetry

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Nonparametric robustness (62G35) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Convex bodies generated by sublinear expectations of random vectors ⋮ Halfspace depth for general measures: the ray basis theorem and its consequences ⋮ Illumination Depth ⋮ Tukey Depths and Hamilton--Jacobi Differential Equations ⋮ Choosing among notions of multivariate depth statistics ⋮ Depth and outliers for samples of sets and random sets distributions ⋮ Simple halfspace depth ⋮ Half-space depth of log-concave probability measures ⋮ Threshold for the expected measure of the convex hull of random points with independent coordinates ⋮ Another look at halfspace depth: flag halfspaces with applications ⋮ On bodies floating in equilibrium in every orientation ⋮ Estimating the probability that a given vector is in the convex hull of a random sample ⋮ Threshold for the expected measure of random polytopes ⋮ Reconstruction of atomic measures from their halfspace depth ⋮ A note on volume thresholds for random polytopes ⋮ Scatter halfspace depth: geometric insights. ⋮ Separation bodies: a conceptual dual to floating bodies ⋮ Barycentric cuts through a convex body ⋮ Affine invariant maps for log-concave functions ⋮ Combining dependent tests based on data depth with applications to the two-sample problem for data of arbitrary types

Uses Software

• robustbase
• RobStatTM

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