A local maximal inequality under uniform entropy

A.W. van der Vaart, J.A. Wellner

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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.
Original languageEnglish
Pages (from-to)192-203
Number of pages12
JournalElectronic Journal of Statistics
Volume5
DOIs
Publication statusPublished - 2011

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