发表机构
University of Chicago; Illinois Institute of Technology（芝加哥大学; 伊利诺伊理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究时间序列中共形预测的覆盖有效性，提出无需混合假设的误差界与中心极限定理，并处理长期记忆情形，揭示时间依赖对覆盖不确定性的影响。
AI 中文摘要
共形预测提供了边际覆盖保证，然而实践者可能想知道观测到的覆盖是否真正异常或与抽样变异一致。实现覆盖的推断受到的关注相对较少，尤其是对于时间序列。我们研究了具有相邻校准集和测试集的时序相关数据的分割共形预测。利用函数依赖性度量，我们在没有混合假设的情况下推导了边际覆盖误差的非渐近界，这些混合假设可能难以验证，甚至对于简单的短记忆模型也可能失效。我们建立了Bahadur表示，据我们所知，这首次为时间依赖下分割共形预测的实现覆盖推导出中心极限定理。基于块的标准误差一致估计量产生了一个渐近合理的检验。我们进一步研究了在共形预测中仍未得到充分研究的长期记忆时间序列。对于高斯线性过程，我们展示了非常强的时间依赖性如何导致实现覆盖的非高斯极限定律，并建立了具有估计归一化的块采样推断。所得理论解释了时间依赖性如何改变覆盖不确定性。
英文摘要
Conformal prediction provides marginal coverage guarantees, yet practitioners may wonder if the observed coverage is truly abnormal or consistent with sampling variation. Inference for realized coverage has received comparatively little attention, especially for time series. We study split conformal prediction with adjacent calibration and test sets of temporally dependent data. Using the functional dependence measure, we derive non-asymptotic bounds on marginal coverage error without mixing assumptions, which can be difficult to verify and may fail even for simple short-memory models. We establish a Bahadur representation to derive, to our knowledge, the first central limit theorem for realized coverage of split conformal prediction under temporal dependence. A consistent block-based estimator of the standard error yields an asymptotically justified test. We further study long-memory time series, which remain understudied in conformal prediction. For Gaussian linear processes, we show how very strong temporal dependence can lead to a non-Gaussian limiting law of realized coverage and establish block-sampling inference with an estimated normalization. The resulting theory explains how temporal dependence changes coverage uncertainty.
