title: Finite sampling inequalities: an application to two-sample Kolmogorov-Smirnov statistics.
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) and by Massart (1990) for one-sample versions of these statistics.
authors.affiliation: Department of Statistics, University of Washington, Seattle, WA 98195-4322.
authors.forename: Evan
authors.initials: E
authors.lastname: Greene
authors.affiliation: Department of Statistics, University of Washington, Seattle, WA 98195-4322.
authors.forename: Jon A
authors.initials: JA
authors.lastname: Wellner
keywords: Bennett inequality; Hoeffding inequality; Kolmogorov-Smirnov statistics; exponential bounds; finite sampling; hypergeometric distribution; two-samples