Bridging centrality and extremity: refining empirical data depth using extreme value statistics

DOI10.1214/15-AOS1359zbMath1327.62205arXiv1510.08694MaRDI QIDQ892256

Jun Li, John H. J. Einmahl, Regina Y. Liu

Publication date: 18 November 2015

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

Full work available at URL: https://arxiv.org/abs/1510.08694

zbMATH Keywords

depthextremesnonparametric classificationtailnonparametric multivariate SPC

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Nonparametric estimation (62G05) Applications of statistics in engineering and industry; control charts (62P30) Statistics of extreme values; tail inference (62G32)

Related Items

Illumination Depth ⋮ Nonparametric Fusion Learning for Multiparameters: Synthesize Inferences From Diverse Sources Using Data Depth and Confidence Distribution ⋮ Affine invariant integrated rank-weighted statistical depth: properties and finite sample analysis ⋮ Tukey’s Depth for Object Data ⋮ Unnamed Item ⋮ On multivariate separating Hill estimator under estimated location and scatter ⋮ Nonparametric Imputation by Data Depth ⋮ Halfspace depth and floating body ⋮ Extreme value theory for anomaly detection -- the GPD classifier ⋮ Halfspace depth does not characterize probability distributions

Cites Work

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• Estimation of extreme risk regions under multivariate regular variation
• A moment estimator for the index of an extreme-value distribution
• On a notion of data depth based on random simplices
• Multivariate spacings based on data depth. I: Construction of nonparametric multivariate tolerance regions
• The random Tukey depth
• Rates of growth and sample moduli for weighted empirical processes indexed by sets
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• A simple general approach to inference about the tail of a distribution
• Projection-based depth functions and associated medians
• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• General notions of statistical depth function.
• Multivariate quantiles and multiple-output regression quantiles: from \(L_{1}\) optimization to halfspace depth
• New nonparametric tests of multivariate locations and scales using data depth
• Control Charts for Multivariate Processes
• On a Geometric Notion of Quantiles for Multivariate Data
• Notions of Limiting P Values Based on Data Depth and Bootstrap
• Regression Depth
• A Quality Index Based on Data Depth and Multivariate Rank Tests
• DD-Classifier: Nonparametric Classification Procedure Based onDD-Plot
• The convex hull of a random set of points
• Regularly varying functions