We propose a general and flexible procedure for testing multiple hypotheses about sequential (or streaming) data that simultaneously controls both the false discovery rate (FDR) and false nondiscovery rate (FNR) under minimal assumptions about the data streams, which may differ in distribution and dimension and be dependent. All that is needed is a test statistic for each data stream that controls its conventional type I and II error probabilities, and no information or assumptions are required about the joint distribution of the statistics or data streams. The procedure can be used with sequential, group sequential, truncated, or other sampling schemes. The procedure is a natural extension of Benjamini and Hochberg’s (1995 Benjamini, Y. and Hochberg, Y. (1995). Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing, Journal of the Royal Statistical Society, Series B: Methodological 57: 289–300. doi:10.1111/j.2517-6161.1995.tb02031.x[Crossref] , [Google Scholar]) widely used fixed sample size procedure to the domain of sequential data, with the added benefit of simultaneous FDR and FNR control that sequential sampling affords. We prove the procedure’s error control and give some tips for implementation in commonly encountered testing situations.

我们提出了一种通用且灵活的程序，用于测试有关顺序（或流）数据的多个假设，这些假设在有关数据流的最小假设下可以同时控制错误发现率（FDR）和错误未发现率（FNR），这可能在分布和分布上有所不同。尺寸和依赖。所有需要的是控制每个数据流的常规I和II型错误概率的测试统计信息，并且不需要有关统计信息或数据流的联合分布的信息或假设。该过程可以与顺序，组顺序，截断或其他采样方案一起使用。该程序是Benjamini和Hochberg（1995 Benjamini，Y.和Hochberg，Y.（1995）。控制错误发现率：一种实用且有效的多重测试方法，皇家统计学会杂志，系列B：方法论57：289 – 300。doi：10.1111 / j.2517-6161.1995.tb02031.x [Crossref]  ，[Google Scholar]）在顺序数据范围内广泛使用了固定样本大小程序，并具有顺序采样所提供的同时FDR和FNR控制的附加好处。我们证明了该过程的错误控制，并提供了一些在常见的测试情况下实施的技巧。