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

Evan Greene and Jon A. Wellner

Stochastic Processes and their Applications, 2016, vol. 126, issue 12, 3701-3715

Abstract: 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.

Keywords: Bennett inequality; Finite sampling; Hoeffding inequality; Hypergeometric distribution; Two-samples; Kolmogorov–Smirnov statistics; Exponential bounds (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:12:p:3701-3715

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DOI: 10.1016/j.spa.2016.04.020

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