标题： 统一箱线图：多重检验的视角 显示英文标题

标题： Unifying Boxplots: A Multiple Testing Perspective

摘要： Tukey的箱形图是探索性数据分析的基础工具，但其经典异常值标记规则未考虑样本量，随后的修改通常被作为独立的启发式调整来呈现。 在本文中，我们提出一个统一的框架，将箱形图及其变体重新视为多重检验程序的图形实现。 我们证明Tukey的原始方法等价于未校正的过程，而现有的考虑样本量的修改对应于控制家庭误差率（FWER）或每族误差率（PFER）。 这一观点不仅系统化了现有方法，还自然地引出了更自适应的新构造。 我们引入了一个基于错误发现率（FDR）的箱形图，并展示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整合到箱形图的图形格式中。 通过将经典的图形工具与多重检验的原则联系起来，我们的工作为比较、批判和扩展现代探索性分析中的异常值检测规则提供了有根据的语言。 显示英文摘要

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.