In online multiple testing, an a priori unknown number of hypotheses are tested sequentially, i.e. at each time point a test decision for the current hypothesis has to be made using only the data available so far. Although many powerful test procedures have been developed for online error control in recent years, most of them are designed solely for independent or at most locally dependent test statistics. In this work, we provide a new framework for deriving online multiple test procedures which ensure asymptotical (with respect to the sample size) control of the familywise error rate (FWER), regardless of the dependence structure between test statistics. In this context, we give a few concrete examples of such test procedures and discuss their properties. Furthermore, we conduct a simulation study in which the type I error control of these test procedures is also confirmed for a finite sample size and a gain in power is indicated.

翻译：在线多重检验中，假设数量先验未知且需按序检验，即每个时间点需仅基于当前可用数据对当前假设做出检验决策。尽管近年已开发出众多用于在线错误控制的检验方法，但大多数方法仅适用于独立或至多局部相依的检验统计量。本研究提出一种新的框架，用于推导可确保家族wise错误率（FWER）渐近（相对于样本量）控制的在线多重检验方法，且不受检验统计量间相依结构的影响。在此框架下，我们给出了若干具体检验方法实例并探讨其性质。此外，我们通过仿真研究验证了这些检验方法在有限样本量下的第一类错误控制效果，并显示出其功效的提升。