Abstract In a multiple testing setting, we consider testing n null hypotheses, denoted by H 1 , … , H n , with the corresponding p-values P i for each H i . We propose a new method which ‘scans’ all intervals in the unit interval [ 0 , 1 ] , selects the longest interval with estimated false discovery rate not exceeding the target level, and then rejects a hypothesis if its p -value is contained in this interval. In contrast, the Benjamini–Hochberg method, which is a threshold-type procedure, does the same but over intervals with an endpoint at the origin. Following Storey et al. (2004), we show that our procedure controls the false discovery rate in an asymptotic sense. We also investigate its asymptotic false non-discovery rate, deriving conditions under which it outperforms the Benjamini–Hochberg procedure. This happens, for example, in power-law location models.

中文翻译：

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用于多重测试的扫描程序：超越阈值类型程序

摘要 在多重测试环境中，我们考虑测试 n 个零假设，用 H 1 , … , H n 表示，每个 H i 具有相应的 p 值 P i 。我们提出了一种新方法，它“扫描”单位区间 [ 0 , 1 ] 中的所有区间，选择估计错误发现率不超过目标水平的最长区间，然后拒绝假设，如果它的 p 值包含在这个区间中间隔。相比之下，Benjamini-Hochberg 方法是一种阈值类型的过程，它执行相同的操作，但在起点处具有端点的间隔。继 Storey 等人之后。(2004)，我们表明我们的程序在渐近意义上控制了错误发现率。我们还研究了它的渐近错误未发现率，得出它优于 Benjamini-Hochberg 程序的条件。发生这种情况，例如，