The LIL for canonical \(U\)-statistics

DOI10.1214/07-AOP351zbMath1144.60015arXivmath/0604262MaRDI QIDQ2427056

Rafał Latała, Radosław Adamczak

Publication date: 15 May 2008

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604262

zbMATH Keywords

law of the iterated logarithmU-statistics

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05)

Related Items (2)

The mathematical work of Evarist Giné ⋮ The LIL for \(U\)-statistics in Hilbert spaces

Cites Work

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• On integrability in the LIL for degenerate \(U\)-statistics
• Moment inequalities for U-statistics
• Asymptotic distribution of symmetric statistics
• Domination inequality for martingale transforms of a Rademacher sequence
• A remark on convergence in distribution of \(U\)-statistics
• Sub-Bernoulli functions, moment inequalities and strong laws for nonnegative and symmetrized \(U\)-statistics
• Necessary and sufficient conditions for the strong law of large numbers for \(U\)-statistics.
• The LIL for canonical \(U\)-statistics of order 2
• On the law of the iterated logarithm for canonical \(U\)-statistics and processes
• Bounds on the tail probability of 𝑈-statistics and quadratic forms
• Tail and moment estimates for some types of chaos
• A Class of Statistics with Asymptotically Normal Distribution
• The Theory of Unbiased Estimation

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