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.

翻译：本文针对顺序变点分析中一个基础但尚未充分探索的挑战：在检测到变化后如何进行推断。我们开发了一个非常通用的框架，仅利用在数据依赖的停止时间（即任意顺序检测算法在该时刻宣告变化）之前观测到的数据，为未知变点构建置信集。该框架是非参数的，对复合后变化类、观测空间或使用的顺序检测过程不做任何假设，并且具有非渐近有效性。我们还在适当假设下将其扩展至处理复合前变化类，并在参数设定下推导出变化幅度的置信集。我们提供了置信区间宽度的理论保证。大量模拟实验表明，生成的置信集规模合理且覆盖率略偏保守。总之，我们提出了首个具有理论可靠性且在实践中广泛适用的顺序变点定位通用方法。