In this paper we consider online multiple testing with familywise error rate (FWER) control, where the probability of committing at least one type I error shall remain under control while testing a possibly infinite sequence of hypotheses over time. Currently, Adaptive-Discard (ADDIS) procedures seem to be the most promising online procedures with FWER control in terms of power. Now, our main contribution is a uniform improvement of the ADDIS principle and thus of all ADDIS procedures. This means, the methods we propose reject as least as much hypotheses as ADDIS procedures and in some cases even more, while maintaining FWER control. In addition, we show that there is no other FWER controlling procedure that enlarges the event of rejecting any hypothesis. Finally, we apply the new principle to derive uniform improvements of the ADDIS-Spending and ADDIS-Graph.

翻译：本文研究基于族系错误率（FWER）控制的在线多重检验问题，即在持续检验可能无限序列的假设过程中，需将至少发生一次第一类错误的概率控制在预设范围内。目前，自适应丢弃（ADDIS）程序在基于FWER控制的在线检验中，其统计功效表现最为突出。本研究的主要贡献在于对ADDIS原理进行了统一改进，从而优化了所有ADDIS程序。具体而言，我们提出的方法在保持FWER控制的前提下，能够拒绝至少与ADDIS程序同样多的假设，某些情况下甚至更多。此外，我们证明了不存在其他FWER控制程序能够扩大拒绝任意假设的事件域。最后，我们将这一新原理应用于ADDIS-Spending和ADDIS-Graph方法，推导出其统一改进形式。