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：与给定闭检验程序兼容的同时置信区间通常缺乏信息性。更精确地说，对于单侧零假设，无论点估计与零假设偏差多大，同时置信区间的边界可能始终紧贴零假设边界。这一点已在Bonferroni-Holm和fall-back程序中得到验证，现有研究提出了无此缺陷的替代性同时置信区间。这些信息性同时置信区间虽与初始多重检验不完全兼容，但接近该检验从而具有相近的势优势。它们能够提供强族系错误率控制的多重假设检验，可替代初始多重检验。本文将对信息性同时置信区间的先前研究拓展至图形检验程序。研究表明，新提出的同时置信区间所获得的信息量始终随反对零假设的证据增强而增加。新同时置信区间在信息获取与尽可能多地拒绝假设目标之间提供了折衷方案。该同时置信区间通过对偶图形族与投影方法定义，并给出了计算该区间的简单迭代算法。模拟研究针对复杂图形检验程序展示了结果。