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Maximum Tests Are Adaptive Permutation Tests, Markus Neuhäeuser, Ludwig A. Hothorn
Maximum Tests Are Adaptive Permutation Tests, Markus Neuhäeuser, Ludwig A. Hothorn
Journal of Modern Applied Statistical Methods
In some areas, e.g., statistical genetics, it is common to apply a maximum test, where the maximum of several competing test statistics is used as a new statistic, and the permutation distribution of the maximum is used for inference. Here, it is shown that maximum tests are special cases of adaptive permutation tests. The 30-year old idea of adaptive statistical tests is more flexible than previously thought when permutation tests are used, and the selector statistic is calculated for every permutation. Because the independence between the selector and the test statistics is no longer needed, the test statistics themselves can …