On the behavior of Tukey's depth and median under symmetric stable distributions.

DOI10.1016/j.jspi.2003.06.017zbMath1040.62038OpenAlexW2045073553MaRDI QIDQ1429880

D. Massart

Publication date: 27 May 2004

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2003.06.017

zbMATH Keywords

RobustnessInfluence functionTukey's medianMinimax biasGross error sensitivityMultivariate medianContamination biasHalfspace depthHalfspace median

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Asymptotic properties of nonparametric inference (62G20) Nonparametric robustness (62G35) Characterization and structure theory for multivariate probability distributions; copulas (62H05)

Related Items

On weighted and locally polynomial directional quantile regression, Uniform convergence rates for the approximated halfspace and projection depth, Halfspace depth and floating body, Learning with correntropy-induced losses for regression with mixture of symmetric stable noise, Halfspace depth does not characterize probability distributions, Scatter halfspace depth for \(K\)-symmetric distributions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• General notions of statistical depth function.
• Structural properties and convergence results for contours of sample statistical depth functions.
• The influence function and maximum bias of Tukey's median
• Projection estimates of multivariate location
• Influence function and maximum bias of projection depth based estimators.
• Lower bounds for contamination bias: Globally minimax versus locally linear estimation
• Robust Estimation of a Location Parameter
• Influence function of halfspace depth
• The depth function of a population distribution.