Max-Type Rank Tests, U-Tests, and Adaptive Tests for the Two-Sample Location Problem - An Asymptotic Power Study

Abstract

For the two-sample location problem we first consider two types of tests, linear rank tests with various scores, but also some tests based on U-statistics. For both types we construct adaptive tests as well as max-type tests and investigate their asymptotic and finite power properties. It turns out that both the adaptive tests have larger asymptotic power than the max-type tests. For small sample sizes, however, some of the max-type tests are to prefer. Ustatistics are convenient if extreme densities may occur.