Empirical depth processes

DOI10.1007/BF02595423zbMath1160.62350OpenAlexW2145269997WikidataQ105583346 ScholiaQ105583346MaRDI QIDQ2474780

Miguel A. Arcones, Heng-Jian Cui, YiJun Zuo

Publication date: 6 March 2008

Published in: Test (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02595423

zbMATH Keywords

empirical projection depth processes

Mathematics Subject Classification ID

Multivariate analysis (62H99) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Nonparametric robustness (62G35) Central limit and other weak theorems (60F05) Inference from stochastic processes (62M99)

Related Items (3)

Nonparametric statistics of dynamic networks with distinguishable nodes ⋮ Asymptotics of generalized depth-based spread processes and applications ⋮ Projection based scatter depth functions and associated scatter estimators

Cites Work

• Limit theorems for \(U\)-processes
• Asymptotics for the Tukey median
• Some extensions of Tukey's depth function
• On a notion of data depth based on random simplices
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• Finite sample breakdown points of projection based multivariate location and scatter statistics
• Projection-based depth functions and associated medians
• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• Depth weighted scatter estimators
• Estimators related to \(U\)-processes with applications to multivariate medians: Asymptotic normality
• General notions of statistical depth function.
• Asymptotics for the Tukey depth process, with an application to a multivariate trimmed mean
• On the Stahel-Donoho estimator and depth-weighted means of multivariate data.
• Weak convergence and empirical processes. With applications to statistics
• Some remarks on the uniform weak convergence of stochastic processes
• Approximation Theorems of Mathematical Statistics
• Uniform Central Limit Theorems
• The Behavior of the Stahel-Donoho Robust Multivariate Estimator
• The depth function of a population distribution.
• Unnamed Item

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