发表机构
Statistical Laboratory, University of Cambridge; Department of Data Sciences and Operations, University of Southern California; Department of Statistics, University of Chicago（剑桥大学统计实验室; 南加州大学数据科学与操作系; 芝加哥大学统计学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对缺失数据下的总体均值置信区间构建，采用可实现污染模型，刻画适应未知污染比例等参数的最小最大长度，并给出达到最优速率的显式有限样本有效自适应区间，且对因果推断有启示。
AI 中文摘要
我们考虑当观测值存在缺失时，总体均值的置信区间构建问题。为适应比完全随机缺失（MCAR）更一般的缺失机制，我们采用Ma等人（2026）的可实现污染模型的一种重新参数化版本，该模型是同一基础分布$P$的MCAR版本与缺失非随机版本的混合。我们刻画了能够适应模型中潜在未知参数（包括污染比例）的置信区间的最小最大长度，这些结果适用于高斯基础分布以及满足特定尾部或对称性假设的非参数类别。在所有这些设定下，我们提供了简单、实用且有限样本有效的自适应置信区间的显式构造，这些区间达到相应的最小最大速率。最后，我们给出了我们的结果对因果推断的启示。
英文摘要
We consider the construction of confidence intervals for population means when observations are subject to missingness. To accommodate more general missingness mechanisms than missing completely at random (MCAR), we adopt a reparametrised version of the realisable contamination model of Ma et al. (2026), which is a mixture of an MCAR version and a missing not at random version of the same base distribution $P$. We characterise the minimax length of confidence intervals that can adapt to potentially unknown parameters of the model, including the contamination fraction, for Gaussian base distributions and for nonparametric classes satisfying certain tail or symmetry assumptions. In all of these settings, we provide explicit constructions of simple, practical and finite-sample valid adaptive confidence intervals that attain the corresponding minimax rates. Finally, we provide implications of our results for causal inference.
Comments64 pages, 5 figures
