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.

翻译：变点定位旨在为变点（若存在）提供置信集。现有方法要么依赖强参数假设，要么仅提供渐近保证，要么专注于特定类型的变化（如均值变化）而非整体分布变化。\cite{dandapanthula2025conformal} 近期提出了一种（可能是首个）实现有限样本有效性的无分布变点定位方法。然而，尽管他们证明了有限样本覆盖性，但未分析集合大小。本文中，我们为其算法提供了严格的理论保证。我们还证明了变点点估计量的一致性，并在无分布假设下推导了其收敛速率。基于此，我们进一步构建了无分布一致性检验，用于判断特定时间点是否为变点。因此，我们的工作为变点检测、定位与检验提供了统一的无分布理论保证。此外，我们展示了分布变化场景下保形$p$值的多种有限样本与渐近性质，为保形$p$值的众多应用奠定了理论基础。作为这些性质的应用，我们构建了针对可交换性相对于分布变化备择假设的无分布一致性检验，并提出了一种新的、计算可行的保形检验功效优化方法。我们通过详尽的模拟研究验证了所提方法与理论结果的性能。综上，我们的贡献为无分布变点推断提供了全面且理论严谨的研究框架，拓展了保形方法在现代变点分析中的适用范围与可信度。