The Benjamini-Hochberg (BH) procedure is a celebrated method for multiple testing with false discovery rate (FDR) control. In this paper, we consider large-scale distributed networks where each node possesses a large number of p-values and the goal is to achieve the global BH performance in a communication-efficient manner. We propose that every node performs a local test with an adjusted test size according to the (estimated) global proportion of true null hypotheses. With suitable assumptions, our method is asymptotically equivalent to the global BH procedure. Motivated by this, we develop an algorithm for star networks where each node only needs to transmit an estimate of the (local) proportion of nulls and the (local) number of p-values to the center node; the center node then broadcasts a parameter (computed based on the global estimate and test size) to the local nodes. In the experiment section, we utilize existing estimators of the proportion of true nulls and consider various settings to evaluate the performance and robustness of our method.

翻译：Benjani-Hochberg (BH) 程序是使用虚假发现率(FDR)控制进行多次测试的著名方法。 在本文中,我们考虑的是大型分布式网络,每个节点拥有大量的p值,目标是以通信效率高的方式实现全球BH性能。 我们建议每个节点按照真实无损假设的(估计)全球比例进行局部测试,调整测试大小。 在适当的假设下,我们的方法与全球BH 程序基本相同。 受此驱动, 我们为恒点网络开发了一种算法, 每个节点只需向中心节点传输无效物(当地)比例和(当地)p值数量的估计; 中心节点然后将参数(根据全球估计和试验大小计算)传送到本地节点。 在实验部分, 我们使用现有对真实无效物比例的估测算器, 并考虑各种环境来评估我们方法的性能和稳健性。