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 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 the upper bound of the maximum regret. Then, we compare the maximum regret of the proposed shrinkage rule with that of CES and pooling rules when the parameter space 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 that of the CES and pooling rules in certain cases when the parameter space is correctly specified. In addition, we find that the shrinkage rule is robust against misspecifications of the parameter space. Finally, we apply our method to experimental data from the National Job Training Partnership Act Study.

翻译：本研究探讨了基于观测协变量确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给能产生最佳实验结果的治疗方案。相反，在统计估计问题中，收缩估计器是一种常用方法，它将无偏但存在噪声的初步估计值向这些估计值的平均值方向收缩，因为众所周知，收缩估计器的均方误差小于未收缩的估计器。受此启发，我们提出了一种计算上可行的收缩规则，该规则通过最小化最大遗憾的上界来选择收缩因子。然后，我们在参数空间正确设定或误设的情况下，比较了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，收缩规则在许多情况下表现良好，这些发现得到了数值实验的进一步支持。具体而言，我们证明当参数空间正确设定时，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参数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研究》的实验数据。