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

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.