Large deviations of U-empirical Kolmogorov–Smirnov tests and their efficiency

Abstract

Non-degenerate U-empirical Kolmogorov–Smirnov tests are studied and their large deviation asymptotics under the null-hypothesis is described. Several examples of such statistics used for testing goodness-of-fit and symmetry are considered. It is shown how to calculate their local Bahadur efficiency.