Moment inequalities for U-statistics

DOI10.1214/009117906000000476zbMath1123.60009arXivmath/0506026OpenAlexW2061957803MaRDI QIDQ874735

Radosław Adamczak

Publication date: 10 April 2007

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

Full work available at URL: https://arxiv.org/abs/math/0506026

zbMATH Keywords

U-statisticsconcentration of measure

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15)

Related Items (22)

Concentration inequalities, counting processes and adaptive statistics ⋮ The mathematical work of Evarist Giné ⋮ Estimates of moments and tails of Gaussian chaoses ⋮ Jackknife multiplier bootstrap: finite sample approximations to the \(U\)-process supremum with applications ⋮ Logarithmic Sobolev inequalities for finite spin systems and applications ⋮ Exponential inequalities for dependent V-statistics via random Fourier features ⋮ Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails ⋮ Optimal Kernel Selection for Density Estimation ⋮ Ranking and empirical minimization of \(U\)-statistics ⋮ The LIL for canonical \(U\)-statistics ⋮ Higher order concentration of measure ⋮ Rejoinder: On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning ⋮ The LIL for \(U\)-statistics in Hilbert spaces ⋮ A Bernstein-type inequality for functions of bounded interaction ⋮ Unnamed Item ⋮ Higher order concentration for functions of weakly dependent random variables ⋮ Moment inequalities for matrix-valued U-statistics of order 2 ⋮ Concentration inequalities for bounded functionals via log-Sobolev-type inequalities ⋮ Concentration inequalities for polynomials in \(\alpha\)-sub-exponential random variables ⋮ Modified log-Sobolev inequalities, Beckner inequalities and moment estimates ⋮ A note on exponential inequalities for the distribution tails of canonical von Mises' statistics of dependent observations ⋮ Entropy and Concentration

Cites Work

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• Estimates of moments and tails of Gaussian chaoses
• On decoupling, series expansions, and tail behavior of chaos processes
• Moment inequalities for functions of independent random variables
• The LIL for canonical \(U\)-statistics of order 2
• Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses
• Hitting probabilities of killed brownian motion : a study on geometric regularity
• Bounds on the tail probability of 𝑈-statistics and quadratic forms
• New concentration inequalities in product spaces

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