文章基本信息

标题：A local maximal inequality under uniform entropy
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作者：Aad van der Vaart ; Jon A. Wellner
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2011
卷号：5
页码：192-203
DOI：10.1214/11-EJS605
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.