Treatment choice with nonlinear regret
本文提出最小化遗憾的非线性变换的均值，以解决传统均值遗憾规则对抽样不确定性敏感的问题，并推导了有限样本贝叶斯和极小化最优规则的闭式分数，适用于正常回归模型和样本量计算。
Summary Following Savage (1951)and Manski (2004), the literature on statistical treatment choice focuses on the mean of welfare regret. Ignoring other features of the regret distribution, however, can lead to a rule that is sensitive to sampling uncertainty. We propose to minimize the mean of a nonlinear transformation of regret and show that singleton rules are not essentially complete for nonlinear regret. Focusing on mean-square regret, we derive closed-form fractions for finite-sample Bayes and minimax optimal rules. Our approach is grounded in decision theory and extends to limit experiments. The treatment fractions can be viewed as the strength of evidence favouring treatment. We apply our framework to a normal regression model and sample-size calculations.