Asymptotic distribution of two-sample empirical \(U\)-quantiles with applications to robust tests for shifts in location

DOI10.1016/j.jmva.2011.08.014zbMath1250.62021OpenAlexW2073587765MaRDI QIDQ764479

Herold G. Dehling, Roland Fried

Publication date: 13 March 2012

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2011.08.014

zbMATH Keywords

\(U\)-statisticsweak dependenceHodges-Lehmann estimatorabsolutely regular processes

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Nonparametric robustness (62G35) Order statistics; empirical distribution functions (62G30) Functional limit theorems; invariance principles (60F17)

Related Items (10)

On normal approximations for the two-sample problem on multidimensional tori ⋮ Nonparametric confidence intervals for location in time series data ⋮ The Mann-Whitney \(U\)-statistic for \(\alpha\)-dependent sequences ⋮ Rejoinder on: Some recent theory for autoregressive count time series ⋮ Change-Point Detection Under Dependence Based on Two-Sample U-Statistics ⋮ Non‐Parametric Change‐Point Tests for Long‐Range Dependent Data ⋮ Extensions of some classical methods in change point analysis ⋮ TESTING FOR CHANGES IN KENDALL’S TAU ⋮ Comments on: ``Extensions of some classical methods in change point analysis ⋮ Comments on: ``Extensions of some classical methods in change point analysis

Uses Software

• R

Cites Work

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• Robust nonparametric tests for the two-sample location problem
• Bahadur representation for \(U\)-quantiles of dependent data
• A Bahadur-type representation for empirical quantiles of a large class of stationary, possibly infinite-variance, linear processes
• Generalized L-, M-, and R-statistics
• Central limit theorem and the bootstrap for \(U\)-statistics of strongly mixing data
• The almost sure invariance principle for the empirical process of U- statistic structure
• Rigorous statistical procedures for data from dynamical systems
• Central limit theorems for empirical and \(U\)-processes of stationary mixing sequences
• Estimation of the variance of partial sums for \(\rho\)-mixing random variables
• The Bahadur-Kiefer representation for \(U\)-quantiles
• Mann-Whitney test for associated sequences
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• Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation
• Weighted Repeated Median Smoothing and Filtering
• On U-statistics and v. mise? statistics for weakly dependent processes
• On the Strong Law of Large Numbers and Related Results for Quasi-Stationary Sequences
• Limiting behavior of U-statistics for stationary, absolutely regular processes
• Nonparametric Confidence Intervals for a Shift Parameter
• The Wilcoxon Two-sample Statistic on Strongly Mixing processes
• Estimates of Location Based on Rank Tests
• A New Proof of the Bahadur Representation of Quantiles and an Application
• Consistency and Unbiasedness of Certain Nonparametric Tests

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