Two-Sample Tests Based on the Integrated Empirical Process
Abstract Let X 1, …, X m and Y 1, …, Y n be independent random variables, where X 1, …, X m are i.i.d. with continuous distribution function (df) F, and Y 1, …, Y n are i.i.d. with continuous df G. For testing the hypothesis H 0: F = G, we introduce and study analogues of the celebrated Kolmogorov–Smirnov and one- and two-sided Cramér-von Mises statistics that are functionals of a suitably integrated two-sample empirical process. Furthermore, we characterize those distributions for which the new tests are locally Bahadur optimal within the setting of shift alternatives.