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：本文探讨了序贯变点分析中一个基础但尚未充分研究的挑战：在检测到变化后进行统计推断。我们构建了一个非常通用的框架，仅利用截至数据依赖的停止时间（此时任意序贯检测算法宣告变化发生）所观测到的数据，为未知变点构造置信集。该框架具有非参数特性，不依赖于复合变化后类别、观测空间或所用序贯检测程序的任何假设，且具有非渐近有效性。我们进一步将其扩展至在适当假设下处理复合变化前类别，并在参数化设定中推导出变化幅度的置信集。我们为置信区间的宽度提供了理论保证。大量仿真实验表明，所构建的集合具有合理的规模及略偏保守的覆盖概率。总而言之，我们提出了首个通用的序贯变点定位方法，该方法理论严谨且在实践中具有广泛适用性。