无需分布假设，实现序列变化点的精准定位与置信推断。
Distribution-free changepoint localization after sequential change detection
- 基于可 conformal test martingales 构建无分布假设的置信集
- 有限样本下保证正确检测时的覆盖率，且置信集期望大小有界
- 适合对统计推断可靠性要求高的实时监测场景
本文提出一种无分布假设的框架，用于在停止序列变化检测后构建变化点的置信集。已知可 conformal test martingales 可用于检测分布变化，但无法提供变化发生时间的推断。以往方法需预先知道变化前后分布类别，而本文在无需任何分布假设的情况下完成变化点定位。建立了有限样本下的覆盖率保证（条件于正确检测），并给出了置信集条件期望大小的非渐近界。在合适的渐近条件下，证明了置信集条件期望大小保持一致有界，并在模拟和真实数据上展现出强性能。据我们所知，这是首个具有有效后检测覆盖性的通用无分布假设序列变化点定位框架。
原文摘要 · Abstract (English)
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 prove 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 valid post-detection coverage.
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