发表机构
Columbia University; Massachusetts Institute of Technology; University of Southern California（哥伦比亚大学; 麻省理工学院; 南加州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非随机缺失矩阵补全，提出合成最近邻估计器，放宽正性与独立性假设，建立误差界、一致性与渐近推断，模拟验证有效。
AI 中文摘要
我们针对非随机缺失（MNAR）数据下的矩阵补全开发了一个因果框架。借鉴计量经济学面板数据文献中的合成控制方法，我们的方法放宽了MNAR矩阵补全中常见的两个假设：正性和观测指示符的独立性。与传统面板数据模型通常需要预设的块稀疏几何结构不同，我们的框架通过目标特定的局部信息结构适应灵活、异质的观测模式。我们提出了合成最近邻（SNN），一种受局部合成控制启发的估计器，并在适当条件下建立了有限样本逐元素误差界和均值恢复的一致性。我们进一步在异方差噪声下推导了渐近正态性，并开发了可行的逐元素推断。为了估计逐元素噪声方差，我们将相同的局部原理应用于平方结果，在有界噪声下获得一致性，在一般次高斯噪声下获得渐近无偏性。模拟研究在多种缺失设计和观测模式下证实了理论发现。
英文摘要
We develop a causal framework for matrix completion under missing not at random (MNAR) data. Drawing on synthetic controls from the econometric panel data literature, our approach relaxes two assumptions common in MNAR matrix completion: positivity and independence of observation indicators. Unlike traditional panel data models, which often require prescribed block-sparse geometries, our framework accommodates flexible, heterogeneous observation patterns through target-specific local information structures. We propose synthetic nearest neighbors (SNN), a local synthetic-controls-inspired estimator, and establish finite-sample entrywise error bounds and consistency for mean recovery under suitable conditions. We further derive asymptotic normality under heteroskedastic noise and develop feasible entrywise inference. To estimate entry-specific noise variances, we apply the same local principle to squared outcomes, obtaining consistency under bounded noise and asymptotic unbiasedness under general subgaussian noise. Simulation studies corroborate the theoretical findings across a range of missingness designs and observation patterns.
