Ordering directional data: Concepts of data depth on circles and spheres

DOI10.1214/aos/1176348779zbMath0766.62027OpenAlexW2043868810MaRDI QIDQ1206718

Regina Y. Liu, Kesar Singh

Publication date: 1 April 1993

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176348779

zbMATH Keywords

circlespheremediandirectional dataspherical triangleangular simplicial depthangular simplicial medianangular Tukey's deptharc distance depthcenter- outward orderingvon Mises class of distributions

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Geometric probability and stochastic geometry (60D05) Characterization and structure theory for multivariate probability distributions; copulas (62H05)

Related Items (21)

Finite sample breakdown point of Tukey's halfspace median ⋮ An almost sure representation of sample circular median ⋮ Multidimensional medians arising from geodesics on graphs ⋮ 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 ⋮ Weighted lens depth: Some applications to supervised classification ⋮ Nonparametric Fusion Learning for Multiparameters: Synthesize Inferences From Diverse Sources Using Data Depth and Confidence Distribution ⋮ Clustering directional data through depth functions ⋮ Kesar Singh's contributions to statistical methodology ⋮ Characterizing angular symmetry and regression symmetry. ⋮ Multivariate spacings based on data depth. I: Construction of nonparametric multivariate tolerance regions ⋮ Connecting pairwise geodesic spheres by depth: DCOPS ⋮ Halfspace depth and floating body ⋮ A note on simplicial depth function ⋮ A new concept of quantiles for directional data and the angular Mahalanobis depth ⋮ Intrinsic Data Depth for Hermitian Positive Definite Matrices ⋮ A New Estimator of a Circular Median ⋮ On the optimality of the max-depth and max-rank classifiers for spherical data. ⋮ Lower bounds for computing statistical depth.

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