In many scientific applications, hypotheses are generated and tested continuously in a stream. We develop a framework for improving online multiple testing procedures with false discovery rate (FDR) control under arbitrary dependence. Our approach is two-fold: we construct methods via the online e-closure principle, as well as a novel formulation of online compound e-values that is defined through donations. This yields strict power improvements over state-of-the-art e-value and p-value procedures while retaining FDR control. We further derive algorithms that compute the decision at time $t$ in $O(\log t)$ time, and we demonstrate improved empirical performance on synthetic and real data.

翻译：在许多科学应用中，假设检验是连续生成并测试的流式过程。我们开发了一个框架，用于改进在任意相依性下具备错误发现率（FDR）控制的在线多重检验程序。我们的方法分为两方面：一方面通过在线e-闭包原理构建方法，另一方面基于捐赠定义提出一种新颖的在线复合e值公式。这在对FDR保持控制的同时，相较于当前最优的e值和p值程序实现了显著的统计功效提升。我们进一步推导出可在$O(\log t)$时间内计算$t$时刻决策的算法，并在合成数据与真实数据上展示了更优的实证性能。