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：与给定闭式检验程序兼容的同时置信区间通常是非信息性的。更精确地说，对于单侧零假设，无论点估计值与零假设偏离多远，同时置信区间的边界都可能紧贴零假设的边界。这一现象已在Bonferroni-Holm和回退程序中得到说明，目前已提出替代的同时置信区间以消除该缺陷。这些信息性同时置信区间虽不完全与原始多重检验兼容，但与之接近，因而具有相似的势优势。它们能提供控制强族错误率的多重检验，可替代原始多重检验。本文将对信息性同时置信区间的先前研究成果拓展至图形检验程序。结果表明，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。该区间在信息获取与尽可能多地拒绝假设的目标之间达成折衷，通过一系列对偶图和投影法进行定义。本文还提供了计算该区间的简单迭代算法。仿真研究针对一个复杂图形检验程序验证了结果。