Finite sampling inequalities: An application to two-sample Kolmogorov-Smirnov statistics

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Greene, Evan¹  Wellner, Jon A.¹ 

[1] Univ Washington, Dept Stat, Seattle, WA 98195 USA

关键词: Bennett inequality;    Finite sampling;    Hoeffding inequality;    Hypergeometric distribution;    Two-samples;    Kolmogorov-Smirnov statistics;    Exponential bounds;   

DOI  :  10.1016/j.spa.2016.04.020

来源: Elsevier

【 摘 要 】

We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our development complements recent results by Wei and Dudley (2012) concerning exponential bounds for two-sided Kolmogorov Smirnov statistics by giving corresponding results for one-sided statistics with emphasis on adjusted inequalities of the type proved originally by Dvoretzky et al. (1956) [3] and by Massart (1990) for one-sample versions of these statistics. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free