Post-detection inference for sequential changepoint localization

Abstract: This paper addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We study the problem of localizing the changepoint using only the data observed up to a data-dependent stopping time at which a sequential detection algorithm $\mathcal A$ declares a change. We first construct confidence sets for the unknown changepoint when pre- and post-change distributions are assumed to be known. We then extend our framework to composite pre- and post-change scenarios. We impose no conditions on the observation space or on $\mathcal A$ -- we only need to be able to run $\mathcal A$ on simulated data sequences. In summary, this work offers both theoretically sound and practically effective tools for sequential changepoint localization.