Some intriguing properties of Tukey's half-space depth
From MaRDI portal
Publication:654416
DOI10.3150/10-BEJ322zbMath1229.62063arXiv1201.1171OpenAlexW2016312261MaRDI QIDQ654416
Subhajit Dutta, Probal Chaudhuri, Anil Kumar Ghosh
Publication date: 28 December 2011
Published in: Bernoulli (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1201.1171
Characterization and structure theory for multivariate probability distributions; copulas (62H05) Applications of functional analysis in probability theory and statistics (46N30) Graphical methods in statistics (62A09)
Related Items
Finite sample breakdown point of Tukey's halfspace median, Convergence of quantile and depth regions, On the computation of multivariate scenario sets for the skew-\(t\) and generalized hyperbolic families, Choosing among notions of multivariate depth statistics, A weighted localization of halfspace depth and its properties, Depth-weighted Bayes classification, Common multivariate estimators of location and scatter capture the symmetry of the underlying distribution, On weighted and locally polynomial directional quantile regression, Weighted lens depth: Some applications to supervised classification, On smoothness of Tukey depth contours, Half-region depth for stochastic processes, Depth and outliers for samples of sets and random sets distributions, Integrated depth for functional data: statistical properties and consistency, Statistical depth in abstract metric spaces, A Bayesian Approach to Multiple-Output Quantile Regression, On a general definition of depth for functional data, Data depth for measurable noisy random functions, Depth in Infinite-dimensional Spaces, Concentration of the empirical level sets of Tukey's halfspace depth, A centrality notion for graphs based on Tukey depth, Halfspace depth and floating body, A topologically valid definition of depth for functional data, A topologically valid construction of depth for functional data, Depth for curve data and applications, On data depth in infinite dimensional spaces, Half-space mass: a maximally robust and efficient data depth method, Approximate calculation of Tukey's depth and median with high-dimensional data, From Depth to Local Depth: A Focus on Centrality
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Multivariate dispersion, central regions and depth. The lift zonoid approach
- On a notion of data depth based on random simplices
- On the Tukey depth of a continuous probability distribution
- The Tukey and the random Tukey depths characterize discrete distributions
- Nonparametric depth-based multivariate outlier identifiers, and masking robustness properties
- Asymptotics for multivariate trimming
- Breakdown properties of location estimates based on halfspace depth and projected outlyingness
- Projection-based depth functions and associated medians
- Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
- On data depth and distribution-free discriminant analysis using separating surfaces
- General notions of statistical depth function.
- The Tukey depth characterizes the atomic measure
- Sign Tests in Multidimension: Inference Based on the Geometry of the Data Cloud
- The multivariate L 1 -median and associated data depth
- Location–Scale Depth
- On Maximum Depth and Related Classifiers
- A simple test for uniformity of a circular distribution