The design of experiments involves a compromise between covariate balance and robustness. This paper provides a formalization of this trade-off and describes an experimental design that allows experimenters to navigate it. The design is specified by a robustness parameter that bounds the worst-case mean squared error of an estimator of the average treatment effect. Subject to the experimenter's desired level of robustness, the design aims to simultaneously balance all linear functions of potentially many covariates. Less robustness allows for more balance. We show that the mean squared error of the estimator is bounded in finite samples by the minimum of the loss function of an implicit ridge regression of the potential outcomes on the covariates. Asymptotically, the design perfectly balances all linear functions of a growing number of covariates with a diminishing reduction in robustness, effectively allowing experimenters to escape the compromise between balance and robustness in large samples. Finally, we describe conditions that ensure asymptotic normality and provide a conservative variance estimator, which facilitate the construction of asymptotically valid confidence intervals.

翻译：实验设计涉及协变量平衡与稳健性之间的权衡。本文对此权衡进行了形式化描述，并提出一种允许实验者驾驭该权衡的实验设计方案。该设计由一个限制平均处理效应估计量在最坏情况下均方误差的稳健性参数指定。在满足实验者期望的稳健性水平的前提下，该设计旨在同时平衡多个潜在协变量的所有线性函数。较低的稳健性允许实现更高的平衡性。我们证明，在有限样本中，估计量的均方误差受限于潜在结果在协变量上的隐含岭回归损失函数的最小值。在渐近情况下，该设计能够完美平衡数量递增的协变量的所有线性函数，且稳健性损失呈递减趋势，从而在理论上使实验者能在大规模样本中摆脱平衡性与稳健性之间的权衡。最后，我们描述了确保渐近正态性的条件，并给出了保守的方差估计量，为构建渐近有效置信区间提供支持。