Continuity of halfspace depth contours and maximum depth estimators: Diagnostics of depth-related methods

DOI10.1006/jmva.2001.2053zbMath1028.62042OpenAlexW2033381745MaRDI QIDQ1861393

Milos Volauf, Ivan Mizera

Publication date: 16 March 2003

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

Full work available at URL: https://semanticscholar.org/paper/affc302f56f7bd2872778767bdcfaa209c6866b4

zbMATH Keywords

stabilitycontinuitydepthset-valued analysisqualitative robustnessdepth contoursmaximum depth estimators

Mathematics Subject Classification ID

Multivariate analysis (62H99) Nonparametric robustness (62G35) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Set-valued functions (26E25) Set-valued maps in general topology (54C60)

Related Items (15)

Computation of projection regression depth and its induced median ⋮ Halfspace depth for general measures: the ray basis theorem and its consequences ⋮ Depth-based classification method underlain by a remote concentration measure for processing asymmetric data ⋮ Choosing among notions of multivariate depth statistics ⋮ Integrated depth for functional data: statistical properties and consistency ⋮ Simple halfspace depth ⋮ Another look at halfspace depth: flag halfspaces with applications ⋮ Multivariate functional outlier detection ⋮ Halfspace depth and floating body ⋮ Reconstruction of atomic measures from their halfspace depth ⋮ Smooth depth contours characterize the underlying distribution ⋮ Depth-based inference for functional data ⋮ Multivariate Functional Halfspace Depth ⋮ From Depth to Local Depth: A Focus on Centrality ⋮ The deepest regression method

Cites Work

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• Halfplane trimming for bivariate distributions
• Convergence of depth contours for multivariate datasets
• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• Robustness of deepest regression
• Asymptotic distributions of the maximal depth estimators for regression and multivariate location
• On depth and deep points: A calculus.
• Sign Tests in Multidimension: Inference Based on the Geometry of the Data Cloud
• Variational Analysis
• Regression Depth
• A General Qualitative Definition of Robustness
• Robust Statistics

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