We consider controlling the false discovery rate for many tests with unknown correlation structure. Given a large number of hypotheses, false and missing discoveries can plague an analysis. While many procedures have been proposed to control false discovery, they either assume independent hypotheses or lack statistical power. We propose a novel method for false discovery control using null bootstrapping. By bootstrapping from the correlated null, we achieve superior statistical power to existing methods and prove that the false discovery rate is controlled. Simulated examples illustrate the efficacy of our method over existing methods. We apply our proposed methodology to financial asset pricing, where the goal is to determine which "factors" lead to excess returns out of a large number of potential factors.

翻译：我们考虑控制许多相关结构不明的测试的虚假发现率。 在大量假设的情况下,虚假和缺失的发现会困扰一项分析。虽然已经提出了许多程序来控制虚假发现,但它们要么假设独立假设,要么缺乏统计能力。我们提出了一种新颖的方法,用空靴子来控制虚假发现。我们从相关的无效中获取了较高的统计能力,并证明虚假发现率得到了控制。模拟例子说明了我们的方法相对于现有方法的功效。我们将我们建议的方法应用于金融资产定价,目的是确定哪些“因素”会导致大量潜在因素的超额回报。