统一箱线图：一种多重检验视角
Unifying Boxplots: A Multiple Testing Perspective
AI总结：
本文提出统一框架，将箱线图及其变体视为多重检验的图形实现，并引入基于FDR的新箱线图，为离群值检测提供原则性语言。
摘要：
Tukey箱线图是探索性数据分析的基础工具，但其经典的离群值标记规则未考虑样本量，后续的修改通常作为独立的启发式调整提出。在本文中，我们提出了一个统一框架，将箱线图及其变体重新诠释为多重检验过程的图形化实现。我们证明Tukey的原始方法等价于未调整的过程，而现有的样本量感知修改对应于控制族错误率（FWER）或每族错误率（PFER）。这一视角不仅系统化了现有方法，还自然地引出了新的、更具适应性的构造。我们引入了一种基于错误发现率（FDR）的箱线图，并展示了我们的框架如何提供一个灵活的流程，将最先进的稳健估计技术直接集成到箱线图的图形格式中。通过将经典图形工具与多重检验原理联系起来，我们的工作为比较、批判和扩展现代探索性分析的离群值检测规则提供了原则性的语言。
英文摘要：
Tukey's boxplot is a foundational tool for exploratory data analysis, but its classic outlier-flagging rule does not account for the sample size, and subsequent modifications have often been presented as separate, heuristic adjustments. In this paper, we propose a unifying framework that recasts the boxplot and its variants as graphical implementations of multiple testing procedures. We demonstrate that Tukey's original method is equivalent to an unadjusted procedure, while existing sample-size-aware modifications correspond to controlling the Family-Wise Error Rate (FWER) or the Per-Family Error Rate (PFER). This perspective not only systematizes existing methods but also naturally leads to new, more adaptive constructions. We introduce a boxplot motivated by the False Discovery Rate (FDR), and show how our framework provides a flexible pipeline for integrating state-of-the-art robust estimation techniques directly into the boxplot's graphical format. By connecting a classic graphical tool to the principles of multiple testing, our work provides a principled language for comparing, critiquing, and extending outlier detection rules for modern exploratory analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
