Limits of canonical \(U\)-processes and \(B\)-valued \(U\)-statistics

DOI10.1007/BF02214273zbMath0807.60008MaRDI QIDQ1322911

Miguel A. Arcones

Publication date: 28 February 1995

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

zbMATH Keywords

weak convergence\(U\)-statisticsdecouplingcanonical kernels\(U\)-processlaw of a chaos processtype two space

Mathematics Subject Classification ID

Gaussian processes (60G15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (10)

The central limit theorem for \(U\)-processes indexed by Hölder's functions ⋮ The law of the iterated logarithm for empirical processes under absolute regularity ⋮ On the law of the iterated logarithm for canonical \(U\)-statistics and processes ⋮ Weak convergence of stochastic processes indexed by smooth functions ⋮ Some remarks on the uniform weak convergence of stochastic processes ⋮ Weak convergence of convex stochastic processes ⋮ The law of the iterated logarithm and Marcinkiewicz law of large numbers for \(B\)-valued \(U\)-statistics ⋮ Gaussian chaos laws on Banach function spaces ⋮ Characterization of LIL Behavior for Non-DegenerateB-ValuedU-Statistics ⋮ DD-Classifier: Nonparametric Classification Procedure Based onDD-Plot

Cites Work

• Limit theorems for \(U\)-processes
• Empirical processes indexed by Lipschitz functions
• Functional limit theorems for U-processes
• Asymptotic distribution of symmetric statistics
• Decoupling and Khintchine's inequalities for \(U\)-statistics
• On decoupling, series expansions, and tail behavior of chaos processes
• The law of large numbers and the central limit theorem in Banach spaces
• The central limit theorem for stochastic processes
• $UB$-Statistics
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Limits of canonical \(U\)-processes and \(B\)-valued \(U\)-statistics