The Tukey depth characterizes the atomic measure

DOI10.1006/jmva.2001.2052zbMath1028.62040OpenAlexW2064154832MaRDI QIDQ1861391

Gleb A. Koshevoy

Publication date: 16 March 2003

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmva.2001.2052

zbMATH Keywords

halfspace depthdepth contour

Mathematics Subject Classification ID

Nonparametric robustness (62G35) Characterization and structure theory for multivariate probability distributions; copulas (62H05)

Related Items (15)

Exact computation of the halfspace depth ⋮ Choosing among notions of multivariate depth statistics ⋮ On smoothness of Tukey depth contours ⋮ Simple halfspace depth ⋮ Affine invariant integrated rank-weighted statistical depth: properties and finite sample analysis ⋮ Some intriguing properties of Tukey's half-space depth ⋮ On the Tukey depth of a continuous probability distribution ⋮ The Tukey and the random Tukey depths characterize discrete distributions ⋮ Halfspace depth and floating body ⋮ Centerpoints: A Link between Optimization and Convex Geometry ⋮ On the Tukey depth of an atomic measure ⋮ Reconstruction of atomic measures from their halfspace depth ⋮ Smooth depth contours characterize the underlying distribution ⋮ Halfspace depth does not characterize probability distributions ⋮ Second-order accuracy of depth-based bootstrap confidence regions

Cites Work

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• Asymptotics for multivariate trimming
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• Halfspace depth and regression depth characterize the empirical distribution
• Halfplane trimming for bivariate distributions
• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• Asymptotic distributions of the maximal depth estimators for regression and multivariate location

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