Multivariate spatial U-quantiles: A Bahadur-Kiefer representation, a Theil-Sen estimator for multiple regression, and a robust dispersion estimator
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Publication:2480022
DOI10.1016/j.jspi.2007.05.043zbMath1131.62049OpenAlexW2026703455MaRDI QIDQ2480022
Weihua Zhou, Robert J. Serfling
Publication date: 28 March 2008
Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jspi.2007.05.043
Characterization and structure theory for multivariate probability distributions; copulas (62H05) Strong limit theorems (60F15) Nonparametric inference (62G99)
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Cites Work
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- Limit theorems for \(U\)-processes
- Bahadur-Kiefer-type processes
- The finite-sample breakdown point of the Oja bivariate median and of the corresponding half-samples version
- Trimmed slope estimates for simple linear regression
- Probability inequalities for empirical processes and a law of the iterated logarithm
- Breakdown points of affine equivariant estimators of multivariate location and covariance matrices
- Descriptive statistics for multivariate distributions
- Glivenko-Cantelli properties of some generalized empirical DF's and strong convergence of generalized L-statistics
- Generalized order statistics, Bahadur representations, and sequential nonparametric fixed-width confidence intervals
- Multivariate location estimation using extension of \(R\)-estimates through \(U\)-statistics type approach
- Asymptotics for \(M\)-estimators defined by convex minimization
- Reduced U-statistics and the Hodges-Lehmann estimator
- A Bernstein-type inequality for \(U\)-statistics and \(U\)-processes
- Incomplete generalized \(L\)-statistics
- On the efficiency of multivariate spatial sign and rank tests
- A general approach to Bahadur-Kiefer representations for \(M\)-estimators
- Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
- The Bahadur-Kiefer representation for \(U\)-quantiles
- General notions of statistical depth function.
- Nonparametric multivariate descriptive measures based on spatial quantiles
- Weak convergence and empirical processes. With applications to statistics
- On the \(u\)\,th geometric conditional quantile
- Generalized multivariate rank type test statistics via spatial U-quantiles
- On a Geometric Notion of Quantiles for Multivariate Data
- Approximation Theorems of Mathematical Statistics
- Multivariate spatial sign and rank methods
- Some properties of incomplete U-statistics
- Uniform Central Limit Theorems
- Alternatives to the Median Absolute Deviation
- Quantile functions for multivariate analysis: approaches and applications
- The multivariate L 1 -median and associated data depth
- Probability Inequalities for Sums of Bounded Random Variables
- A Note on Quantiles in Large Samples
- On Bahadur's Representation of Sample Quantiles
- Estimates of the Regression Coefficient Based on Kendall's Tau
- Sequential Confidence Intervals Based on Rank Tests
- Estimates of Location Based on Rank Tests
- A New Proof of the Bahadur Representation of Quantiles and an Application
- Efficient and Robust Fitting of Lognormal Distributions
- Nonparametric notions of multivariate scatter measure and more scattered based on statistical depth functions
- On affine equivariant multivariate quantiles