Adaptive tests for the c-sample location problem - The case of two-sided alternatives

In the c-sample location problem the classical F-test is the appropriate test under the model of normality. For nonnormal data, however, there are rank tests which have higher power than the F-test, e.g. the Gastwirth test for symmetric distributions with short tails or the Hogg-Fisher-Randles test for asymmetric distributions. But usually the practicing statistician has no information about the underlying distribution. Therefore, an adaptive test should be applied which takes the given data set into account. Two versions of such an adaptive test are proposed including a new test for distributions with long tails. These adaptive tests are compared with each of the single rank tests in the adaptive scheme and also with the classical F-test. It is shown via Monte Carlo simulation that the adaptive tests behave well over a broad class of distributions.