发表机构
Georgia State University; University of Waterloo; Massachusetts Institute of Technology（佐治亚州立大学; 滑铁卢大学; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对序贯数据中的多重检验问题，提出基于e值和检验超鞅的序贯重置程序，在FDR控制下定位失效区间，并给出两种设置下的明确界限，应用于LLM水印检测和金融回测。
AI 中文摘要
数据按序到达，每个数据点与一个零假设相关联。我们开发了检验程序，以在错误发现率（FDR）控制下定位某些零假设失效的区间。这些新程序被称为序贯重置程序，它们基于e值和检验超鞅。我们还通过在每个拒绝块中检验超鞅的块最小值之前丢弃信息量较少的数据点，开发了这些程序的改进版本。这些程序在两种设置下具有明确的FDR界限：经典的独立性设置，以及零数据与非零数据之间可能存在依赖的更一般设置。这些FDR界限与检验时间范围无关，一般性界限具有任意时点有效性，但相比标准FDR水平多了一个对数因子。我们展示了模拟研究和数据实验，将序贯重置程序应用于LLM水印检测和金融回测。
英文摘要
Data arrive sequentially, each associated with a null hypothesis. We develop testing procedures to locate intervals in which some null hypotheses fail with false discovery rate (FDR) control. The new procedures are called sequential resetting procedures, and they are based on e-values and test supermartingales. We also develop a refined version of the procedures by dropping less informative data points before the block minimum of the test supermartingale in each rejection block. These procedures have explicit FDR bounds under two settings: a classic setting of independence and the more general setting of possible dependence across null data and non-null data. These FDR bounds are independent of the testing horizon, and the general one has anytime validity, but it has an extra logarithm factor compared with the standard FDR level. We present simulation studies and data experiments with applications of sequential resetting procedures to LLM watermark detection and financial backtesting.
Comments67 pages
