Moderate deviations for degenerate \(U\)-processes.

DOI10.1016/S0304-4149(99)00112-XzbMath1045.60029MaRDI QIDQ1877398

Peter Eichelsbacher

Publication date: 7 September 2004

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

Bernstein-type inequalitymoderate deviationsdecouplingHoeffding decompositionVapnik-Červonenkis class\(U\)-statistics, \(U\)-processes\(V\)-processes

Mathematics Subject Classification ID

Large deviations (60F10) Sample path properties (60G17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Cites Work

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• U-processes: Rates of convergence
• Limit theorems for \(U\)-processes
• On a notion of data depth based on random simplices
• Functional limit theorems for U-processes
• Probabilities of large deviations in topological spaces. II
• Decoupling and Khintchine's inequalities for \(U\)-statistics
• Large deviations, moderate deviations and LIL for empirical processes
• Sharper bounds for Gaussian and empirical processes
• \(U\)-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of \(U\)-statistics with estimated parameters
• Rank-dependent moderate deviations of \(U\)-empirical measures in strong topologies
• Moderate and large deviations for \(U\)-processes
• Moderate deviations of dependent random variables related to CLT
• On the law of the iterated logarithm for canonical \(U\)-statistics and processes
• Moderate Deviations and Associated Laplace Approximations for Sums of Independent Random Vectors
• Probability Inequalities for Sums of Bounded Random Variables
• A Class of Statistics with Asymptotically Normal Distribution
• Convergence of stochastic processes