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2011 A local maximal inequality under uniform entropy
Aad van der Vaart, Jon A. Wellner
Electron. J. Statist. 5: 192-203 (2011). DOI: 10.1214/11-EJS605


We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant δ. The bound is expressed in the uniform entropy integral of the class at δ. The bound yields a rate of convergence of minimum contrast estimators when applied to the modulus of continuity of the contrast functions.


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Aad van der Vaart. Jon A. Wellner. "A local maximal inequality under uniform entropy." Electron. J. Statist. 5 192 - 203, 2011.


Published: 2011
First available in Project Euclid: 14 April 2011

zbMATH: 1268.60027
MathSciNet: MR2792551
Digital Object Identifier: 10.1214/11-EJS605

Primary: 60K35

Keywords: empirical process , minimum contrast estimator , modulus of continuity , rate of convergence

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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