A local maximal inequality under uniform entropy
Aad van der Vaart and Jon A. Wellner
Source: Electron. J. Statist. Volume 5
(2011), 192-203.
Abstract
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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Permanent link to this document: http://projecteuclid.org/euclid.ejs/1302784853
Digital Object Identifier: doi:10.1214/11-EJS605
Mathematical Reviews number (MathSciNet): MR2792551
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