有限样本下的量化目标最小化遗憾治疗规则
Minimax regret treatment rules with finite samples when a quantile is the object of interest
AI总结：
本文研究了在有限样本下，针对结果分布特定分位数的最小化遗憾治疗规则，发现当分位数超过1/2时，永远不治疗最优；当分位数小于1/2时，总是治疗最优。
摘要：
考虑一个决策者通过有限样本了解总体，并基于该样本决定是否应用某种治疗的设定。我们研究了在不同抽样方案下，当结果被限制在单位区间时，有限样本最小化遗憾治疗规则。与Stoye（2009）关注最大化期望效用不同，本文关注的是结果分布的特定分位数。我们发现，当样本包含固定数量的未治疗和已治疗单位时，任何治疗规则都是最小化遗憾最优的。同样，在样本中随机分配治疗且任何分配概率的情况下，也是如此。当已知的未治疗总体分位数等于1/2时，情况也相同。然而，如果已知的分位数超过1/2，则永远不治疗是唯一最优的规则；如果分位数小于1/2，则总是治疗是最佳的。我们还考虑了包含协变量的情况。
英文摘要：
Consider a setup in which a decision maker is informed about the population by a finite sample and based on that sample has to decide whether or not to apply a certain treatment. We work out finite sample minimax regret treatment rules under various sampling schemes when outcomes are restricted onto the unit interval. In contrast to Stoye (2009) where the focus is on maximization of expected utility the focus here is instead on a particular quantile of the outcome distribution. We find that in the case where the sample consists of a fixed number of untreated and a fixed number of treated units, any treatment rule is minimax regret optimal. The same is true in the case of random treatment assignment in the sample with any assignment probability and in the case of testing an innovation when the known quantile of the untreated population equals 1/2. However if the known quantile exceeds 1/2 then never treating is the unique optimal rule and if it is smaller than 1/2 always treating is optimal. We also consider the case where a covariate is included.
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