The optimal power puzzle: scrutiny of the monotone likelihood ratio assumption in multiple testing
最优功效之谜：审视多重检验的单调似然比假设
In single hypothesis testing, power is a non-decreasing function of type I error rate; hence it is desirable to test at the nominal level exactly to achieve optimal power. The puzzle lies in the fact that for multiple testing, under the false discovery rate paradigm, such a monotonic relationship may not hold. In particular, exact false discovery rate control may lead to a less powerful testing procedure if a test statistic fails to fulfil the monotone likelihood ratio…