Weak convergence and Glivenko-Cantelli results for empirical processes of U-statistic structure

DOI10.1016/0304-4149(89)90046-XzbMath0685.60037MaRDI QIDQ1826203

Wilhelm Schneemeier

Publication date: 1989

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

zbMATH Keywords

weak convergenceempirical processesVapnik-Chervonenkis classes

Mathematics Subject Classification ID

Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items

\(U\)-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of \(U\)-statistics with estimated parameters, On an independence test approach to the goodness-of-fit problem, A central limit theorem for two-sample U-processes

Cites Work

• Unnamed Item
• U-processes: Rates of convergence
• Generalized L-, M-, and R-statistics
• Probability inequalities for empirical processes and a law of the iterated logarithm
• Convergence of a class of empirical distribution functions of dependent random variables
• Glivenko-Cantelli properties of some generalized empirical DF's and strong convergence of generalized L-statistics
• Central limit theorems for empirical measures
• On large deviations of the empiric D.F. of vector chance variables and a law of the iterated logarithm
• Probability Inequalities for Sums of Bounded Random Variables