发表机构
University of Warwick; ESSEC Business School（华威大学; 法国高等经济商业学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究从含噪声、部分观测的张量数据估计双线性形式，信号遵循Tucker2模型。针对交错采用设计的缺失模式，提出谱算法，证明非渐近均方误差界并扩展到一般设计，最后经实验验证理论发现。
AI 中文摘要
我们研究从有噪声、部分观测的张量数据中估计双线性形式。信号遵循Tucker2模型，张量层和切片特定核心具有共享单位和时间因素。缺失模式由交错采用设计构成，常见于因果推断及相关应用。首先分析四模块缺失模式，提出一种跨层汇集信息并直接针对函数的谱算法，而非补全整个张量。证明了非渐近均方误差界，其在层数上呈现相变，展示汇集何时改善估计，并与局部极小极大下界匹配。然后通过锚定四模块约简将构造扩展到一般交错采用设计，得出类似理论保证。最后通过模拟和真实数据集实验验证理论结果。
英文摘要
We study the estimation of bilinear forms from noisy, partially observed multilayer data. The signal follows a Tucker2 model, with shared unit and time factors across tensor layers and slice-specific cores. The missingness pattern is structured and motivated by staggered adoption designs, which are common in causal inference and related applications. We first analyze the four-block missingness pattern, the basic building block for general staggered adoption, and propose a spectral algorithm that pools information across layers and targets the functional directly. We prove a non-asymptotic mean squared error bound that exhibits a phase transition in the number of layers, showing when pooling improves estimation, and match it with a local minimax lower bound up to constants when ranks and logarithmic factors are treated as constant-order quantities. We then extend the construction to general staggered adoption designs via an anchored four-block reduction, and derive analogous theoretical guarantees. Finally, we validate our theoretical findings using synthetic and real-world data on Castle Doctrine laws and COVID-19 policies
Comments108 pages, 12 figures, 3 tables
