Multidimensional trimming based on projection depth

DOI10.1214/009053606000000713zbMath1106.62057arXivmath/0702655OpenAlexW1969901539MaRDI QIDQ869968

YiJun Zuo

Publication date: 12 March 2007

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

Full work available at URL: https://arxiv.org/abs/math/0702655

zbMATH Keywords

robustnessasymptoticsefficiencyinfluence functionbreakdown pointdepth regionsdirectional radiusmultivariate trimmed means

Mathematics Subject Classification ID

Multivariate analysis (62H99) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Nonparametric robustness (62G35)

Related Items (21)

Choosing among notions of multivariate depth statistics ⋮ A new approach for the computation of halfspace depth in high dimensions ⋮ Data depth trimming counterpart of the classical \(t\) (or \(T^2\)) procedure ⋮ Computing projection depth and its associated estimators ⋮ Non-asymptotic analysis and inference for an outlyingness induced winsorized mean ⋮ Depth-weighted means of noisy data: an application to estimating the average effect in heterogeneous panels ⋮ Least sum of squares of trimmed residuals regression ⋮ High dimensional data analysis using multivariate generalized spatial quantiles ⋮ Trimmed and winsorized standard deviations based on a scaled deviation ⋮ A note on weak convergence of general halfspace depth trimmed means ⋮ K-sign depth: from asymptotics to efficient implementation ⋮ The Tukey and the random Tukey depths characterize discrete distributions ⋮ Trimmed and Winsorized means based on a scaled deviation ⋮ Asymptotics of generalized depth-based spread processes and applications ⋮ Local mutual information for dissimilarity-based image segmentation ⋮ On the Tukey depth of an atomic measure ⋮ On depth measures and dual statistics. A methodology for dealing with general data ⋮ On data depth in infinite dimensional spaces ⋮ The random Tukey depth ⋮ Robustness of the deepest projection regression functional ⋮ Trimmed and Winsorized transformed means based on a scaled deviation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Breakdown points of affine equivariant estimators of multivariate location and covariance matrices
• On a notion of data depth based on random simplices
• Asymptotics for multivariate trimming
• Limit theorems for the simplicial depth
• The metrically trimmed mean as a robust estimator of location
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• Descriptive statistics for nonparametric models. II: Location
• Do robust estimators work with real data?
• Finite sample breakdown points of projection based multivariate location and scatter statistics
• A note on Tyler's modification of the MAD for the Stahel-Donoho estimator
• Projection-based depth functions and associated medians
• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• Asymptotic distributions of the maximal depth estimators for regression and multivariate location
• 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.
• Influence function and maximum bias of projection depth based estimators.
• Weak convergence and empirical processes. With applications to statistics
• Robustness of weighted \(L^p\)-depth and \(L^p\)-median
• The asymptotic distribution of the trimmed mean
• Approximation Theorems of Mathematical Statistics
• On Some Robust Estimates of Location
• The 1972 Wald Lecture Robust Statistics: A Review
• Relations between Weak and Uniform Convergence of Measures with Applications
• Robust Statistics
• Convergence of stochastic processes

This page was built for publication: Multidimensional trimming based on projection depth