Max-type rank tests, U-tests, and adaptive tests for the two-sample location problem -- An asymptotic power study

For the two-sample location problem, two types of tests are considered, linear rank tests with various scores, but also some tests based on U-statistics. For both types adaptive tests as well as max-type tests are constructed and their asymptotic and finite power properties are investigated. It turns out that both the adaptive tests have a larger asymptotic power than the max-type tests. For small sample sizes, however, some of the max-type tests are preferable. U-statistics are convenient if extreme densities may occur.Adaptive tests U-statistics Max-type tests Linear rank tests Asymptotic power