A local maximal inequality under uniform entropy

DOI10.1214/11-EJS605zbMath1268.60027arXiv1012.5533OpenAlexW1997817606WikidataQ41920973 ScholiaQ41920973MaRDI QIDQ1952182

Jon A. Wellner, Aad W. van der Vaart

Publication date: 28 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.5533

zbMATH Keywords

rate of convergencemodulus of continuityempirical processminimum contrast estimator

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Inequalities; stochastic orderings (60E15) Functional limit theorems; invariance principles (60F17) Foundations of stochastic processes (60G05)

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Cites Work

• Risk bounds for statistical learning
• A central limit theorem under metric entropy with \(L_ 2\) bracketing
• Central limit theorems for empirical measures
• Rates of convergence for minimum contrast estimators
• The method of sieves and minimum contrast estimators
• Weak convergence and empirical processes. With applications to statistics
• Concentration inequalities and asymptotic results for ratio type empirical processes
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