A local maximal inequality under uniform entropy

Aad van der Vaart; Jon A. Wellner

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arXiv · 1012.5533

A local maximal inequality under uniform entropy

Aad van der Vaart·Jon 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.

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Aad van der Vaart, Jon A. Wellner. 2010-12-26. A local maximal inequality under uniform entropy. https://arxiv.org/abs/1012.5533

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