An estimate on the supremum of a nice class of stochastic integrals and U-statistics

DOI10.1007/s00440-005-0440-9zbMath1128.62063arXivmath/0310324OpenAlexW2040933569MaRDI QIDQ877452

Péter Major

Publication date: 23 April 2007

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310324

zbMATH Keywords

degenerate U-statisticssupremum bounds

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Inequalities; stochastic orderings (60E15) Stochastic integrals (60H05)

Related Items (13)

Laws of the iterated logarithm for the local U-statistic process ⋮ Partial identification and inference in censored quantile regression ⋮ On kernel-based estimation of conditional Kendall's tau: finite-distance bounds and asymptotic behavior ⋮ Ranking and empirical minimization of \(U\)-statistics ⋮ Risk bounds when learning infinitely many response functions by ordinary linear regression ⋮ Concentration inequalities for two-sample rank processes with application to bipartite ranking ⋮ Unnamed Item ⋮ Nonparametric Estimation of the Multivariate Distribution Function in a Censored Regression Model with Applications ⋮ Uniform asymptotics for kernel density estimators with variable bandwidths ⋮ Breaking the curse of dimensionality in nonparametric testing ⋮ Unnamed Item ⋮ Central limit theorem for multiple integrals with respect to the empirical process ⋮ Conditional independence testing via weighted partial copulas

Cites Work

• The central limit theorem for empirical processes on Vapnik- Červonenkis classes
• Limit theorems for \(U\)-processes
• Some limit theorems for empirical processes (with discussion)
• Strong embedding of the estimator of the distribution function under random censorship
• Inequalities in Fourier analysis
• \(U\)-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of \(U\)-statistics with estimated parameters
• Convergence of stochastic processes
• Unnamed Item

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