提出首个通用方法，在检测到变化后给出变化点的置信区间。
Post-detection inference for sequential changepoint localization
- 基于检测时刻的数据，构建变化点的非参数置信集。
- 无需假设分布形式，理论保证覆盖概率且区间合理。
- 适用于任意检测算法，适合实际应用中的在线分析。
本文针对序列变化点分析中一个基础但长期被忽视的问题——检测后进行推断——提出了一个通用框架，仅利用在任意序列检测算法触发变化时所观测到的数据，构建未知变化点的置信集。该框架为非参数方法，不依赖于变化后分布类、观测空间或检测过程的假设，且具有非渐近有效性。我们还将其扩展至处理复合前变化类（需满足合适假设），并在参数设定下推导出变化幅度的置信集。理论证明了置信区间的宽度控制能力。大量模拟实验表明，所得置信集大小合理，覆盖概率略偏保守。综上，本文首次提出一种理论上严谨、广泛适用的序列变化点定位方法。
原文摘要 · Abstract (English)
This paper addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We develop a very general framework to construct confidence sets for the unknown changepoint using only the data observed up to a data-dependent stopping time at which an arbitrary sequential detection algorithm declares a change. Our framework is nonparametric, making no assumption on the composite post-change class, the observation space, or the sequential detection procedure used, and is non-asymptotically valid. We also extend it to handle composite pre-change classes under a suitable assumption, and also derive confidence sets for the change magnitude in parametric settings. We provide theoretical guarantees on the width of our confidence intervals. Extensive simulations demonstrate that the produced sets have reasonable size, and slightly conservative coverage. In summary, we present the first general method for sequential changepoint localization, which is theoretically sound and broadly applicable in practice.
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