In causal inference with panel data under staggered adoption, the goal is to estimate and derive confidence intervals for potential outcomes and treatment effects. We propose a computationally efficient procedure, involving only simple matrix algebra and singular value decomposition. We derive non-asymptotic bounds on the entrywise error, establishing its proximity to a suitably scaled Gaussian variable. Despite its simplicity, our procedure turns out to be instance-optimal, in that our theoretical scaling matches a local instance-wise lower bound derived via a Bayesian Cram\'{e}r-Rao argument. Using our insights, we develop a data-driven procedure for constructing entrywise confidence intervals with pre-specified coverage guarantees. Our analysis is based on a general inferential toolbox for the SVD algorithm applied to the matrix denoising model, which might be of independent interest.

翻译：在交错采用情形下的面板数据因果推断中，目标是估计潜在结果和处理效应并推导其置信区间。我们提出了一种计算高效的方法，仅涉及简单的矩阵代数和奇异值分解。我们推导了逐个误差的非渐近界，证明了其与适当缩放的高斯变量的接近性。尽管方法简单，它实际上是实例最优的，因为我们的理论缩放与通过贝叶斯克拉美-罗论证推导的局部实例下界相匹配。基于我们的洞见，我们开发了一种数据驱动方法，用于构建具有预设覆盖保证的逐个置信区间。我们的分析基于一个通用的推断工具箱，该工具箱适用于矩阵去噪模型中的SVD算法，这可能具有独立的研究价值。