Refined asymptotic Kolmogorov-Smirnov tests for the case of finite support

Abstract

We derive asymptotic critical values for the one-sample and two-sample Kolmogorov-Smirnov tests in the case where the distribution or distributions have finite support of known size. When the number of points in the support is small, these critical values are significantly smaller than those for the standard Kolmogorov-Smirnov tests, thus leading to a major increase in power. We also examine how the asymptotic critical values perform for small sample sizes, finding that they typically lead to conservative inference procedures.