A new concept of quantiles for directional data and the angular Mahalanobis depth

DOI10.1214/14-EJS904zbMath1349.62197OpenAlexW1967250030MaRDI QIDQ2015161

Christophe Ley, Thomas Verdebout, Camille Sabbah

Publication date: 23 June 2014

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ejs/1402927498

zbMATH Keywords

Bahadur representationdirectional statisticsMahalanobis depthrotationally symmetric distributionsDD- and QQ-plot

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Order statistics; empirical distribution functions (62G30) Applications of statistics to physics (62P35) Graphical methods in statistics (62A09)

Related Items (14)

Diagnostic analysis of a circular-circular regression model using asymmetric or asymmetric bi-modal circular errors ⋮ The GLD-plot: a depth-based graphical tool to investigate unimodality of directional data ⋮ Recent advances in directional statistics ⋮ Best approach direction for spherical random variables ⋮ On the use of \(L\)-functionals in regression models ⋮ Clustering directional data through depth functions ⋮ Distance-based directional depth classifiers: a robustness study ⋮ Spatial quantiles on the hypersphere ⋮ Testing multivariate quantile by empirical likelihood ⋮ Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields ⋮ Halfspace depth and floating body ⋮ Depth for curve data and applications ⋮ On the optimality of the max-depth and max-rank classifiers for spherical data. ⋮ On Optimal Tests for Rotational Symmetry Against New Classes of Hyperspherical Distributions

Cites Work

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• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• Asymptotics in statistics. Some basic concepts.
• On adaptive estimation in stationary ARMA processes
• General notions of statistical depth function.
• Multivariate quantiles and multiple-output regression quantiles: from \(L_{1}\) optimization to halfspace depth
• Robustness, Dispersion, and Local Functions in Data Depth
• On a Geometric Notion of Quantiles for Multivariate Data
• Regression Quantiles
• Quantile functions for multivariate analysis: approaches and applications
• Regression Depth
• Optimal R-estimation of a spherical location
• DD-Classifier: Nonparametric Classification Procedure Based onDD-Plot
• A Note on Quantiles in Large Samples
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