Powerful Two-Sample Tests Based on the Likelihood Ratio

AbstractA new approach to constructing nonparametric tests for the general two-sample problem is proposed. This approach not only generates traditional tests (including the two-sample Kolmogorov–Smirnov, Cramér–von Mises, and Anderson–Darling tests), but also produces new powerful tests based on the likelihood ratio. Although conventional two-sample tests are sensitive to the difference in location, most of them lack power to detect changes in scale and shape. The new tests are location-, scale-, and shape-sensitive, so they are robust against variation in distribution.