Approximate calculation of Tukey's depth and median with high-dimensional data

DOI10.2298/YJOR180520022BzbMath1460.62069arXiv1812.03174WikidataQ129204487 ScholiaQ129204487MaRDI QIDQ4987798

Milica Bogićević, Milan J. Merkle

Publication date: 4 May 2021

Published in: Yugoslav Journal of Operations Research (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.03174

zbMATH Keywords

big datadepth functionsmultivariate medianscomputing Tukey's depth

Mathematics Subject Classification ID

Characterization and structure theory for multivariate probability distributions; copulas (62H05) Robustness and adaptive procedures (parametric inference) (62F35) Nonparametric tolerance and confidence regions (62G15)

Related Items

Tukey Depths and Hamilton--Jacobi Differential Equations ⋮ Uniform convergence rates for the approximated halfspace and projection depth ⋮ Tukey’s Depth for Object Data

Uses Software

• depth
• AS 307
• Quicksort
• ABCDepth

Cites Work

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• Some intriguing properties of Tukey's half-space depth
• Jensen's inequality for multivariate medians
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• Computing depth contours of bivariate point clouds
• High-dimensional computation of the deepest location.
• Exact computation of the halfspace depth
• General notions of statistical depth function.
• Absolute approximation of Tukey depth: theory and experiments
• Multivariate spatial U-quantiles: A Bahadur-Kiefer representation, a Theil-Sen estimator for multiple regression, and a robust dispersion estimator
• Jensen's inequality for medians
• Computing the Discrete Fréchet Distance with Imprecise Input
• Algorithm AS 307: Bivariate Location Depth
• Computing Halfspace Depth and Regression Depth
• The depth function of a population distribution.