This study examines the problem of determining whether to treat individuals based on observed covariates. The most common decision rule is the conditional empirical success (CES) rule proposed by Manski (2004), which assigns individuals to treatments that yield the best experimental outcomes conditional on the observed covariates. Conversely, using shrinkage estimators, which shrink unbiased but noisy preliminary estimates toward the average of these estimates, is a common approach in statistical estimation problems because it is well-known that shrinkage estimators may have smaller mean squared errors than unshrunk estimators. Inspired by this idea, we propose a computationally tractable shrinkage rule that selects the shrinkage factor by minimizing an upper bound of the maximum regret. Then, we compare the maximum regret of the proposed shrinkage rule with those of the CES and pooling rules when the space of conditional average treatment effects (CATEs) is correctly specified or misspecified. Our theoretical results demonstrate that the shrinkage rule performs well in many cases and these findings are further supported by numerical experiments. Specifically, we show that the maximum regret of the shrinkage rule can be strictly smaller than those of the CES and pooling rules in certain cases when the space of CATEs is correctly specified. In addition, we find that the shrinkage rule is robust against misspecification of the space of CATEs. Finally, we apply our method to experimental data from the National Job Training Partnership Act Study.

翻译：本研究探讨了如何根据观测到的协变量决定是否对个体进行治疗的问题。最常见的决策规则是Manski（2004）提出的条件经验成功（CES）规则，该规则根据观测协变量将个体分配到能产生最佳实验结果的处置组。相反，在统计估计问题中，收缩估计量（将无偏但噪声较大的初步估计值向这些估计值的平均值方向收缩）是一种常用方法，因为众所周知，收缩估计量可能比未收缩估计量具有更小的均方误差。受此启发，我们提出一种计算可行的收缩规则，通过最小化最大遗憾的上界来选择收缩因子。随后，我们比较了在条件平均处置效应（CATE）空间被正确设定或误设时，所提出的收缩规则与CES规则及合并规则的最大遗憾。我们的理论结果表明，收缩规则在多数情况下表现良好，这些发现进一步得到了数值实验的支持。具体而言，我们证明当CATE空间被正确设定时，在某些情况下收缩规则的最大遗憾可以严格小于CES规则和合并规则。此外，我们发现收缩规则对CATE空间的误设具有鲁棒性。最后，我们将该方法应用于《国家职业培训合作法案研究》的实验数据。