On the uniform consistency of the zonoid depth

DOI10.1016/j.jmva.2015.09.020zbMath1328.62330OpenAlexW2194806769MaRDI QIDQ900822

Miguel López-Díaz, Ignacio Cascos

Publication date: 23 December 2015

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

Full work available at URL: https://doi.org/10.1016/j.jmva.2015.09.020

zbMATH Keywords

uniform consistencyzonoid depth

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Asymptotic properties of nonparametric inference (62G20) Geometric probability and stochastic geometry (60D05)

Related Items (6)

Choosing among notions of multivariate depth statistics ⋮ Some multivariate goodness of fit tests based on data depth ⋮ The zonoid region parameter depth ⋮ Control charts based on parameter depths ⋮ Simultaneous monitoring of origin and scale in left-bounded processes via depth ⋮ Combining dependent tests based on data depth with applications to the two-sample problem for data of arbitrary types

Cites Work

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• On a notion of data depth based on random simplices
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• Lift zonoids, random convex hulls and the variability of random vectors
• Zonoid trimming for multivariate distributions
• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• General notions of statistical depth function.
• Control Charts for Multivariate Processes
• A Quality Index Based on Data Depth and Multivariate Rank Tests
• Isoperimetric inequalities in Euclidean convex bodies
• Theory of Random Sets
• The depth function of a population distribution.

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