We study an online multiple testing problem where the hypotheses arrive sequentially in a stream. The test statistics are independent and assumed to have the same distribution under their respective null hypotheses. We investigate two recently proposed procedures LORD and LOND, which are proved to control the FDR in an online manner. In some (static) model, we show that LORD is optimal in some asymptotic sense, in particular as powerful as the (static) Benjamini–Hochberg procedure to first asymptotic order. We also quantify the performance of LOND. Some numerical experiments complement our theory.

中文翻译：

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关于一些连续多重测试程序的威力

我们研究了一个在线多重测试问题，其中假设在一个流中顺序到达。检验统计量是独立的，并假设在它们各自的零假设下具有相同的分布。我们调查了最近提出的两个程序洛德和伦敦，它们被证明可以在线控制 FDR。在一些（静态）模型中，我们证明了洛德在某种渐近意义上是最优的，特别是与（静态）本杰米尼-霍赫伯格过程到一阶渐近阶一样强大。我们还量化了 LOND 的性能。一些数值实验补充了我们的理论。