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Abstract:
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We consider the problem of simultaneously testing multiple one-sided null hypotheses. It is known that stepwise test procedures (for example, the Holm procedure) are by construction more powerful than their single step counterparts (for example, the Bonferroni test). This power advantage, however, comes only at the cost of increased difficulties in constructing compatible simultaneous confidence intervals for the parameter of interest. They are easily obtained for the Bonferroni method, but surprisingly hard to derive for the Holm procedure, for example. We discuss the inherent problems and show that ad hoc solutions used in practice typically do not control the pre-specified simultaneous confidence level. Instead, we derive simultaneous confidence intervals being compatible with a certain class of closed test procedures using weighted Bonferroni tests for each intersection hypothesis.
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