We propose a general framework based on selectively traversed accumulation rules (STAR) for interactive multiple testing with generic structural constraints on the rejection set. It combines accumulation tests from ordered multiple testing with data-carving ideas from post-selection inference, allowing for highly flexible adaptation to generic structural information. Our procedure defines an interactive protocol for gradually pruning a candidate rejection set, beginning with the set of all hypotheses and shrinking with each step. By restricting the information at each step via a technique we call masking, our protocol enables interaction while controlling the false discovery rate (FDR) in finite samples for any data-adaptive update rule that the analyst may choose. We suggest update rules for a variety of applications with complex structural constraints, show that STAR performs well for problems ranging from convex region detection to FDR control on directed acyclic graphs, and show how to extend it to regression problems where knockoff statistics are available in lieu of $p$-values.

中文翻译：

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结构约束下错误发现率控制的通用交互框架

我们提出了一个基于选择性遍历累积规则（STAR）的通用框架，用于在拒绝集上具有通用结构约束的交互式多重测试。它将有序多重测试的累积测试与选择后推理的数据雕刻思想相结合，允许高度灵活地适应通用结构信息。我们的程序定义了一个交互式协议，用于逐渐修剪候选拒绝集，从所有假设的集合开始，并随着每一步缩小。通过通过我们称为掩码的技术限制每一步的信息，我们的协议在控制分析人员可能选择的任何数据自适应更新规则的有限样本中的错误发现率 (FDR) 的同时实现交互。