arXiv:2608.01691stat.MEcs.AI2026-08

提出ARM方法,精准定位多变量序列中变化的坐标并控制错误率。

ARM: Detector-Agnostic Changepoint Attribution with Finite-Sample Error Control

论文配图:ARM: Detector-Agnostic Changepoint Attribution with Finite-Sample Error Control
图 1 · 摘自论文原文
  • 基于最大分段秩统计量,不依赖检测器精度,自动识别变化坐标。
  • 在高维下保持误差率控制,即使在重尾数据中仍具检验力。
  • 适用于金融、生物等多变量时间序列分析,适合需精确归因的研究者。

检测多变量序列中的变化仅回答了第一个问题;实际操作中更关键的是确定哪些坐标发生了变化。现有方法存在缺陷:块级方法仅对预定义分组提供保证,高维变量选择方法虽可解释但无误差保障,后检测推断则只控制时间轴上的错误率而非坐标间。我们提出ARM(按最大秩归因),作为通用封装器,接收任意检测器找到的变点,输出被认证为发生变化的坐标集合,并附带位置或尺度类型标签。ARM通过各坐标上的最大分段秩统计量评分。由于该统计量在估计分割点处占优,证书对变点估计方式和精度均不变。仅基于坐标内秩,即可获得三项有限样本保证:任意检测器下单坐标有效性;通过保留跨坐标依赖性的Westfall--Young联合置换实现精确全族错误率控制,辅以完全分布自由的Holm备选;在高维且坐标间任意依赖下,通过Benjamini--Yekutieli和e-BH实现假发现率控制。模拟显示,朴素的坐标逐个检验在维度上升时家族错误率超过0.66,而ARM维持名义水平,且在重尾数据中仍有效、高维下具检出力,并能准确标注变化类型。在2008金融危机前后五个金融序列上,ARM将尺度变化归因于每个资产类别,排除了注入的控制坐标。

原文摘要 · Abstract (English)

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.

变点检测错误率控制高维分析

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