Post-detection inference for sequential changepoint localization

• 成果类型: Article; Early Access
• 署名作者: Saha, Aytijhya; Ramdas, Aaditya
• 署名单位: Massachusetts Institute of Technology (MIT); Carnegie Mellon University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkag069
• 发表日期: 2026-04-27
• 关键词: e-processes; postdetection inference; sequential changepoint analysis; change-point; tests; time

摘要

This article 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 postchange class, the observation space, or the sequential detection procedure used, and is nonasymptotically valid. We also extend it to handle composite prechange 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.