标题： 使用共形p值进行变化定位的理论保证 显示英文标题

标题： Theoretical guarantees for change localization using conformal p-values

摘要： 变化点定位旨在为变化点（如果存在的话）提供置信集。 现有方法要么依赖于强参数假设，要么只提供渐近保证，或者专注于某种特定的变化（例如均值变化），而不是整个分布的变化。 最近，\cite{dandapanthula2025conformal}引入了一种方法（可能是第一种）实现了具有有限样本有效性的无分布变化点定位。 然而，虽然他们证明了有限样本覆盖率，但没有对集合大小进行分析。 在本工作中，我们为其算法提供了严格的理论保证。 我们还展示了变化点估计量的一致性，并在没有分布假设的情况下推导了其收敛速率。 沿着这一思路，我们还构建了一个无分布的一致性检验，用于评估某个时间点是否为变化点。 因此，我们的工作为变化点检测、定位和检验提供了统一的无分布保证。 此外，我们介绍了在分布变化设置下共形$p$-值的各种有限样本和渐近性质，这为共形$p$-值的许多应用提供了理论基础。 作为这些性质的应用，我们构建了针对分布变化替代假设的无分布一致性检验，以及一种新的计算上可行的方法来优化共形检验的功效。 我们进行了详细的模拟研究以验证我们方法和理论结果的性能。 总之，我们的贡献提供了一种全面且理论上有根据的方法，用于无分布的变化点推断，拓宽了现代变化点分析中共形方法的适用范围和可信度。 显示英文摘要

摘要： Changepoint localization aims to provide confidence sets for a changepoint (if one exists). Existing methods either relying on strong parametric assumptions or providing only asymptotic guarantees or focusing on a particular kind of change(e.g., change in the mean) rather than the entire distributional change. A method (possibly the first) to achieve distribution-free changepoint localization with finite-sample validity was recently introduced by \cite{dandapanthula2025conformal}. However, while they proved finite sample coverage, there was no analysis of set size. In this work, we provide rigorous theoretical guarantees for their algorithm. We also show the consistency of a point estimator for change, and derive its convergence rate without distributional assumptions. Along that line, we also construct a distribution-free consistent test to assess whether a particular time point is a changepoint or not. Thus, our work provides unified distribution-free guarantees for changepoint detection, localization, and testing. In addition, we present various finite sample and asymptotic properties of the conformal $p$-value in the distribution change setup, which provides a theoretical foundation for many applications of the conformal $p$-value. As an application of these properties, we construct distribution-free consistent tests for exchangeability against distribution-change alternatives and a new, computationally tractable method of optimizing the powers of conformal tests. We run detailed simulation studies to corroborate the performance of our methods and theoretical results. Together, our contributions offer a comprehensive and theoretically principled approach to distribution-free changepoint inference, broadening both the scope and credibility of conformal methods in modern changepoint analysis.