AI 中文总结
本文针对潜在结果有界的有限总体平均处理效应估计问题，提出独立随机分配结合无截距回归的最优实验设计，其最坏情况均方误差优于平衡完全随机化等方法，且可扩展至任意估计量场景。
AI 中文摘要
当潜在结果（如二元结果）已知有界时，本文研究用于估计有限总体平均处理效应的随机实验的最优设计与分析。在所有分配机制和一大类仿射估计量中，最坏情况均方误差（MSE）可通过独立随机分配，以及以支持中点为中心的结果对中心化处理进行无截距的非常规回归实现最小化。这与平衡完全随机化和均值差估计的常规建议形成对比：当结果有界时，实际处理份额中的随机性具有信息价值。与全样本完全随机化相比，最坏情况增益渐近较小，但相对于其他设计可实现一阶增益：完全配对内随机化和配对固定效应回归的最坏情况MSE是前者的两倍。本文将结果扩展至允许任意估计量，独立随机分配仍保持最优，且通常非线性的最优估计量可显著降低最坏情况MSE。
英文摘要
I study the optimal design and analysis of randomized experiments for estimating finite-population average treatment effects when potential outcomes are known to be bounded, as with binary outcomes. Among all assignment mechanisms and a broad class of affine estimators, worst-case mean-squared error (MSE) is minimized by independent random assignment and an unconventional regression of the support-midpoint-centered outcome on the recentered treatment, with no intercept. This contrasts with the usual prescription of balanced complete randomization and difference-in-means estimation: when outcomes are bounded, randomness in the realized treatment share is informative. The worst-case gain over full-sample complete randomization is asymptotically small, but gains can be first-order relative to other designs: complete within-pair randomization and pair-fixed-effect regression have twice the worst-case MSE. I extend the result to allow for arbitrary estimators. Independent random assignment remains optimal, and the generally-nonlinear optimal estimator can meaningfully reduce worst-case MSE.
Comments23 pages, 2 figures
