Shrinkage Methods for Treatment Choice
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处理选择的收缩方法
- 研究问题
- 基于协变量决定是否给予处理时，能否通过收缩噪声较大的条件效应估计，降低决策的最大遗憾并抵御效应空间误设？
- 方法与思路
- 作者通过最小化最大遗憾的上界选择收缩因子，将所得规则与条件经验成功规则及合并规则比较，并使用模拟和培训实验数据。
- 材料陈述的贡献
- 摘要称，效应空间正确设定时，收缩规则在某些情形下具有严格更小的最大遗憾；理论和数值分析也支持其对空间误设的稳健性。
- 阅读关注点
- 应核对条件效应空间的约束、最大遗憾上界的紧致程度、严格改进成立的情形，以及误设稳健性的定义与比较范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要只报告特定情形的优势，未说明普遍支配结论或误设稳健性的边界。
原文摘要
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.