Moderate deviations for degenerate \(U\)-processes.
type: Item
instance of: scholarly article
title: Moderate deviations for degenerate \(U\)-processes.
zbMATH Open document ID: 1045.60029
DOI: 10.1016/S0304-4149(99)00112-X
author: Peter Eichelsbacher
published in: Stochastic Processes and their Applications
publication date: 2004-09-07T00:00:00Z
review text: \(U\)-processes of order \(m\) defined on a probability space \((S,\mathcal S,\mu )\) and indexed by a collection of measurable functions \(\mathcal H\) are considered in case that each function \(h\in \mathcal H\) is completely degenerate (\(\mu \)-canonical). Sufficient conditions on \(\mathcal H \) are established under which the moderate \(U\)-process of rank \(r,\;2\leq r \leq m\), satisfies the moderate deviation principle (MDP). Especially, for \(\mathcal H\) to be Vapnik-Červonenkis subgraph class of function, the MDP is established under exponential moment condition on the envelope of \(\mathcal H .\) Some new Bernstein-type inequalities for \(U\)-processes are proved by using randomization and decoupling technique. Results on MDP for \(V\)-processes are also presented.
reviewed by: Zuzana Prášková
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 2098078
zbMATH Keywords: moderate deviations
zbMATH Keywords: \(U\)-statistics, \(U\)-processes
zbMATH Keywords: \(V\)-processes
zbMATH Keywords: decoupling
zbMATH Keywords: Vapnik-Červonenkis class
zbMATH Keywords: Hoeffding decomposition
zbMATH Keywords: Bernstein-type inequality
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2098078