Multivariate spacings based on data depth. I: Construction of nonparametric multivariate tolerance regions

DOI10.1214/07-AOS505zbMath1360.62253arXiv0806.2970MaRDI QIDQ930655

Regina Y. Liu, Jun Li

Publication date: 1 July 2008

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

Full work available at URL: https://arxiv.org/abs/0806.2970

zbMATH Keywords

data depthdepth order statisticsmultivariate spacingsstatistically equivalent blockstolerance region

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Asymptotic properties of nonparametric inference (62G20) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Nonparametric tolerance and confidence regions (62G15) Order statistics; empirical distribution functions (62G30)

Related Items (20)

A multivariate control quantile test using data depth ⋮ Nonparametric Tests for Homogeneity of Species Assemblages: A Data Depth Approach ⋮ Regression Tolerance Intervals ⋮ Some multivariate goodness of fit tests based on data depth ⋮ Multivariate tests of uniformity ⋮ Conditional predictive inference for stable algorithms ⋮ An approach for specifying trimming and winsorization cutoffs ⋮ A new nonparametric lack-of-fit test of nonlinear regression in presence of heteroscedastic variances ⋮ Bridging centrality and extremity: refining empirical data depth using extreme value statistics ⋮ Nonparametric Fusion Learning for Multiparameters: Synthesize Inferences From Diverse Sources Using Data Depth and Confidence Distribution ⋮ Statistical depth in abstract metric spaces ⋮ Approximate tolerance intervals for nonparametric regression models ⋮ Consistency and robustness of tests and estimators based on depth ⋮ Some multivariate goodness-of-fit tests based on data depth ⋮ Consistency of the likelihood depth estimator for the correlation coefficient ⋮ New robust tests for the parameters of the Weibull distribution for complete and censored data ⋮ Distribution-Free Prediction Sets ⋮ Data-driven nonparametric tolerance sets ⋮ Adaptive exponential power depth with application to classification ⋮ Predictive inference for bivariate data: combining nonparametric predictive inference for marginals with an estimated copula

Uses Software

• Qhull

Cites Work

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• On a Class of Problems Related to the Random Division of an Interval
• An Extension of Wilks' Method for Setting Tolerance Limits
• A Bivariate Sign Test

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