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 regression 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：多重检验领域现有研究主要处理p值之间的三种相依假设：独立性、正向回归相依及任意相依。本文首次在多种负相依概念（负高斯相依、负回归相依、负关联、负象限相依及弱负相依）下给出理论结果。我们研究了Simes全局零假设检验和Benjamini-Hochberg程序，已知实验表明这些方法在负相依下呈现保守性不足。这些程序的保守性不足程度受限于比任意相依情形更小的因子（特别是与检验假设数量无关的因子）。我们还提供了负相依e值的新结果，并给出多个负相依可能产生的实例。本文证明过程初等且简洁，因此易于推广与扩展。最后提出我们研究为解决若干紧迫问题所开启的学术窗口。