Sub-Bernoulli functions, moment inequalities and strong laws for nonnegative and symmetrized \(U\)-statistics

DOI10.1214/aop/1022677268zbMath0951.60028OpenAlexW1984564363MaRDI QIDQ1807183

Cun-Hui Zhang

Publication date: 9 November 1999

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

Full work available at URL: https://doi.org/10.1214/aop/1022677268

zbMATH Keywords

\(U\)-statisticssub-Bernoulli functionsstrong law of large numberdistribution inequalities

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15)

Related Items (5)

Necessary and sufficient conditions for the strong law of large numbers for \(U\)-statistics. ⋮ The LIL for canonical \(U\)-statistics of order 2 ⋮ The Poisson binomial distribution -- old \& new ⋮ The LIL for canonical \(U\)-statistics ⋮ Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications

Cites Work

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• Limit theorems for \(U\)-processes
• Convergence of self-normalized generalized \(U\)-statistics
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• On \(L^p\)-convergence of \(U\)-statistics
• A remark on convergence in distribution of \(U\)-statistics
• Order of magnitude bounds for expectations of \(\Delta_2\)-functions of nonnegative random bilinear forms and generalized \(U\)-statistics
• Decoupling inequalities for the tail probabilities of multivariate \(U\)- statistics
• Laws of large numbers for quadratic forms, maxima of products and truncated sums of i.i.d. random variables
• On the almost sure minimal growth rate of partial sum maxima
• Strong law of large numbers for sums of products
• Approximation Theorems of Mathematical Statistics

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