\(U\)-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of \(U\)-statistics with estimated parameters

DOI10.1016/0304-4149(94)90098-1zbMath0807.62014OpenAlexW1977418064MaRDI QIDQ1336984

Miguel A. Arcones, Evarist Giné M.

Publication date: 8 November 1994

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(94)90098-1

zbMATH Keywords

empirical processeslaw of the iterated logarithmexponential inequalitiesbootstrap central limit theoremU-processestrimming of U-statisticsU-statistics with estimated parametersVapnik- Cervonenkis classesVC classes of functions

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

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Cites Work

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• Limit theorems for \(U\)-processes
• The law of the iterated logarithm for \(U\)-processes
• Probability inequalities for empirical processes and a law of the iterated logarithm
• Bootstrapping general empirical measures
• Weak and strong representations for trimmed U-statistics
• Glivenko-Cantelli properties of some generalized empirical DF's and strong convergence of generalized L-statistics
• Log log laws for empirical measures
• On the asymptotic normality of statistics with estimated parameters
• On the bootstrap of \(U\) and \(V\) statistics
• Decoupling and Khintchine's inequalities for \(U\)-statistics
• Asymptotic normality of U-statistics based on trimmed samples
• On the effect of substituting parameter estimators in limiting \(\chi ^ 2U\) and V statistics
• Weak convergence and Glivenko-Cantelli results for empirical processes of U-statistic structure
• Bootstrapping u - statistics with estimated parameters
• Testing the Hypothesis That Two Populations Differ Only in Location
• A New Proof of the Bahadur Representation of Quantiles and an Application
• Convergence of stochastic processes