A Two-Sample Adaptive Distribution-Free Test

An adaptive distribution-free test is proposed for the two-sample location problem. First, the data are used to assess the tailweight and skewness of the underlying distributions. This leads to the selection and then application, with the same data, of one of several common rank tests for shift, such as the Mann-Whitney-Wilcoxon test. The preliminary selection is made in a way that insures the testing procedure is distribution-free. A Monte Carlo study shows that the adaptive test has excellent power over a wide class of distributions and is preferable to certain prominent nonadaptive tests.

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