On smoothness of Tukey depth contours

DOI10.1080/02331888.2016.1145680zbMath1359.62165OpenAlexW2330922298WikidataQ115917871 ScholiaQ115917871MaRDI QIDQ2953448

Irène Gijbels, Stanislav Nagy

Publication date: 4 January 2017

Published in: Unnamed Author (Search for Journal in Brave)

Full work available at URL: https://lirias.kuleuven.be/handle/123456789/564562

zbMATH Keywords

smoothnessquasi-concavitydata depthTukey depthdepth contoursoptimal halfspace

Mathematics Subject Classification ID

Density estimation (62G07) Nonparametric robustness (62G35) Characterization and structure theory for multivariate probability distributions; copulas (62H05)

Related Items (4)

Tukey Depths and Hamilton--Jacobi Differential Equations ⋮ On weighted and locally polynomial directional quantile regression ⋮ Halfspace depth and floating body ⋮ The limit of finite sample breakdown point of Tukey's halfspace median for general data

Cites Work

• 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
• Smooth depth contours characterize the underlying distribution
• 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
• General notions of statistical depth function.
• The Tukey depth characterizes the atomic measure
• Asymptotics for the Tukey depth process, with an application to a multivariate trimmed mean
• Mathematical Analysis
• Influence function of halfspace depth

This page was built for publication: On smoothness of Tukey depth contours