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

被引：4

作者：

Greene, Evan ^{[1
]}

Wellner, Jon A. ^{[1
]}

机构：

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

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2016年 / 126卷 / 12期

基金：

美国国家科学基金会;

关键词：

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

D O I：

10.1016/j.spa.2016.04.020

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：3701 / 3715

页数：15

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