Simultaneous confidence intervals (SCIs) that are compatible with a given closed test procedure are often non-informative. More precisely, for a one-sided null hypothesis, the bound of the SCI can stick to the border of the null hypothesis, irrespective of how far the point estimate deviates from the null hypothesis. This has been illustrated for the Bonferroni-Holm and fall-back procedures, for which alternative SCIs have been suggested, that are free of this deficiency. These informative SCIs are not fully compatible with the initial multiple test, but are close to it and hence provide similar power advantages. They provide a multiple hypothesis test with strong family-wise error rate control that can be used in replacement of the initial multiple test. The current paper extends previous work for informative SCIs to graphical test procedures. The information gained from the newly suggested SCIs is shown to be always increasing with increasing evidence against a null hypothesis. The new SCIs provide a compromise between information gain and the goal to reject as many hypotheses as possible. The SCIs are defined via a family of dual graphs and the projection method. A simple iterative algorithm for the computation of the intervals is provided. A simulation study illustrates the results for a complex graphical test procedure.

翻译：与给定封闭检验程序兼容的同步置信区间（SCIs）通常是非信息性的。更准确地说，对于单边零假设，无论点估计值与零假设的偏离程度如何，SCI的边界都可能紧贴零假设的边界。这一现象已在Bonferroni-Holm和fall-back程序中得到说明，针对这些程序已有替代性SCIs被提出，这些方法避免了上述缺陷。这些信息性SCIs与初始多重检验并非完全兼容，但非常接近，因此能提供相似的检验功效优势。它们提供了一种具有强族系错误率控制的多重假设检验，可替代初始多重检验。本文扩展了先前关于信息性SCIs的研究，将其应用于图形检验程序。新提出的SCIs所获得的信息量被证明总是随着否定零假设的证据增强而增加。新SCIs在信息增益与尽可能拒绝更多假设的目标之间提供了折衷方案。这些SCIs通过双重图族和投影方法定义。文中提供了计算区间的简单迭代算法。模拟研究通过复杂图形检验程序的结果验证了该方法的有效性。