ARM：具有有限样本误差控制的检测器无关变点归因方法

中文摘要 AI 辅助

检测多元序列中的变化仅回答了两个问题中的第一个，实际问题是哪些坐标发生了变化。现有解决方案并不完善：块级方法在加性联合边界下验证预定义的坐标组，高维变量选择方法返回可解释的排名但无误差保证，检测后推理文献在时间轴而非坐标维度控制误差。我们提出ARM（Attribution by Rank Maxima，基于秩最大值的归因），这是一个包装器，可接受任意检测器定位的变点，并返回经认证发生变化的坐标集合，每个坐标带有位置或尺度类型标签。ARM通过跨分割最大值秩统计量对每个坐标打分，由于该统计量优于估计分割处的对应统计量，所得认证对变点估计的方式和准确性均不敏感。仅通过坐标内秩即可得到三个有限样本保证：在任意检测器下的单坐标有效性；通过保留跨坐标依赖的Westfall–Young联合置换实现精确的家族式误差控制，并有完全分布自由的Holm fallback；以及通过Benjamini–Yekutieli和e-BH在高维任意坐标依赖下的错误发现率控制。在模拟中，在估计变点处进行的朴素单坐标测试随维度增长将其家族式误差放大至超过0.66，而ARM在保持名义水平的同时，还在重尾分布下保持有效性、在高维中具有功效并提供准确的类型标签。在围绕2008年崩溃的五个金融序列上，ARM将尺度变化归因于所有资产类别，并排除了注入的控制坐标。

英文摘要

Detecting a change in a multivariate series answers only the first of two questions; the operational question is which coordinates changed. Existing answers are incomplete. Block-level procedures certify predefined groups of coordinates under an additive union bound, high-dimensional variable-selection methods return interpretable rankings without error guarantees, and the post-detection inference literature controls error along the time axis rather than across coordinates. We propose ARM (Attribution by Rank Maxima), a wrapper that accepts a changepoint located by an arbitrary detector and returns the set of coordinates certified to have changed, each carrying a location or scale type label. ARM scores each coordinate by a max-over-splits rank statistic. Because this statistic dominates the corresponding statistic at the estimated split, the resulting certificate is invariant to the manner, and to the accuracy, of the changepoint estimate. Three finite-sample guarantees follow from within-coordinate ranks alone: per-coordinate validity under any detector; exact family-wise error control through a Westfall--Young joint permutation that preserves cross-coordinate dependence, with a fully distribution-free Holm fallback; and false discovery rate control under arbitrary coordinate dependence in high dimensions through Benjamini--Yekutieli and e-BH. In simulations, naive per-coordinate testing at the estimated changepoint inflates its family-wise error beyond $0.66$ as the dimension grows, whereas ARM maintains the nominal level while retaining validity under heavy tails, power in high dimensions, and accurate type labels. On five financial series surrounding the 2008 collapse, ARM attributes a scale change to every asset class and excludes injected control coordinates.

发表机构

• Beijing University of Technology（北京工业大学）
• Nanyang Technological University（南洋理工大学）
• Sichuan University（四川大学）

机构由 AI 辅助整理，请以论文原文为准。