A local maximal inequality under uniform entropy

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

doi:10.1214/11-EJS605

A local maximal inequality under uniform entropy

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

Mathematics

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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 language	English
Pages (from-to)	192-203
Number of pages	12
Journal	Electronic Journal of Statistics
Volume	5
DOIs	https://doi.org/10.1214/11-EJS605
Publication status	Published - 2011

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AB - 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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JO - Electronic Journal of Statistics

JF - Electronic Journal of Statistics

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A local maximal inequality under uniform entropy

Abstract

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