Connecting pairwise geodesic spheres by depth: DCOPS

DOI10.1016/j.jmva.2018.08.008zbMath1404.60070OpenAlexW2889035271WikidataQ125081226 ScholiaQ125081226MaRDI QIDQ1755114

Leonardo Moreno, Fabrice Gamboa, Ricardo Fraiman

Publication date: 4 January 2019

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

Full work available at URL: https://doi.org/10.1016/j.jmva.2018.08.008

zbMATH Keywords

Riemannian manifoldsgeodesic distancedepth measuresspherical depth

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Nonparametric estimation (62G05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items

Weighted lens depth: Some applications to supervised classification, Level sets of depth measures in abstract spaces, Tukey’s Depth for Object Data, Supervised classification of geometrical objects by integrating currents and functional data analysis, Recent advances in functional data analysis and high-dimensional statistics, Halfspace depth and floating body, Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications

Cites Work

• A partial overview of the theory of statistics with functional data
• Limit theorems for \(U\)-processes
• Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
• On a notion of data depth based on random simplices
• On depth measures and dual statistics. A methodology for dealing with general data
• Descriptive statistics for multivariate distributions
• Ordering directional data: Concepts of data depth on circles and spheres
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• Central limit theorems for empirical measures
• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• Robust covariance and scatter matrix estimation under Huber's contamination model
• A characterization of halfspace depth
• General notions of statistical depth function.
• Empirical processes and applications: An overview. (With discussion)
• Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis
• Lens data depth and median
• Approximation Theorems of Mathematical Statistics
• A multivariate von mises distribution with applications to bioinformatics
• Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh
• The multivariate L ₁ -median and associated data depth
• Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging
• Robust principal component analysis based on trimming around affine subspaces
• On power and sample size determinations for the Wilcoxon–Mann–Whitney test
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• Riemannian Geometry
• Some Fundamental Properties of a Multivariate von Mises Distribution
• VC‐dimension on manifolds: a first approach
• Robust Statistics
• Uniformity in weak convergence
• A General Qualitative Definition of Robustness
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