The multiple testing literature has primarily dealt with three types of dependence assumptions between p-values: independence, positive regression dependence, and arbitrary dependence. In this paper, we provide what we believe are the first theoretical results under various notions of negative dependence (negative Gaussian dependence, negative association, negative orthant dependence and weak negative dependence). These include the Simes global null test and the Benjamini-Hochberg procedure, which are known experimentally to be anti-conservative under negative dependence. The anti-conservativeness of these procedures is bounded by factors smaller than that under arbitrary dependence (in particular, by factors independent of the number of hypotheses tested). We also provide new results about negatively dependent e-values, and provide several examples as to when negative dependence may arise. Our proofs are elementary and short, thus arguably amenable to extensions and generalizations. We end with a few pressing open questions that we think our paper opens a door to solving.

翻译：多重测试文献主要涉及三种不同价值之间的依赖性假设:独立性、正回归依赖性和任意依赖性。在本文中,我们提供了我们认为是各种消极依赖性概念(负高斯依赖性、负关联性、负或过份依赖性和弱负依赖性)下的第一批理论结果。其中包括西梅斯全球无效测试和本杰明-霍奇伯格程序,它们被实验性地认为是消极依赖性下反保守性的。这些程序的反保守性与与任意依赖性下较小的因素(特别是独立于所测试的假设数之外的因素)相联。我们还提供了关于负面依赖性电子价值的新结果,并提供了可能出现的负依赖性依赖性的几个例子。我们的证据是基本的和短的,因此可以说是可以扩展和概括性的。我们最后提出了几个我们认为我们的文件打开了解决之门的紧迫的开放问题。