Distribution-free changepoint localization after sequential change detection
It solves the problem of post-detection changepoint localization without distributional assumptions, which previously required known distribution classes.
This paper develops a distribution-free framework for constructing confidence sets for changepoints after sequential change detection, providing finite-sample coverage guarantees and bounded expected set sizes, with strong empirical performance on simulated and real data.
This paper introduces a distribution-free framework for constructing post-detection confidence sets for changepoints after stopping a sequential change detection procedure. It is well known that conformal test martingales can be used to sequentially detect changes in distribution, but by themselves provide no inference for the time at which a proclaimed change occurred. Past work on post-detection inference requires pre- and post-change classes of distributions to be known, but this paper accomplishes localization of the changepoint without any distributional assumptions. We establish finite-sample coverage guarantees (conditional on correct detection). We provide non-asymptotic bounds on the conditional expected size of the confidence sets. Under suitable asymptotic regimes, we proved that the conditional expected size of the confidence set remains uniformly bounded. and demonstrate strong empirical performance on simulated and real data. To the best of our knowledge, this is the first general distribution-free framework for sequential changepoint localization with a valid post-detection coverage guarantee.