The literature focuses on the mean of welfare regret, which can lead to undesirable treatment choice due to sensitivity 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 favoring treatment. We apply our framework to a normal regression model and sample size calculation.

翻译：文献中主要关注福利遗憾的均值，这可能因对抽样不确定性的敏感性而导致不理想的治疗选择。我们建议最小化遗憾的非线性变换的均值，并表明对于非线性遗憾，单点规则并非本质完备。以均方遗憾为重点，我们推导了有限样本贝叶斯最优规则和极小化极大最优规则的闭式分数。我们的方法基于决策理论，并可扩展至极限实验。治疗分数可被视为支持治疗证据的强度。我们将该框架应用于正态回归模型和样本量计算。