论文标题
当部分确定收益时，最佳决策规则
Optimal Decision Rules when Payoffs are Partially Identified
论文作者
论文摘要
当收益取决于部分识别的参数$θ$时，我们为离散选择问题提供渐近最佳的统计决策规则，而决策者可以使用点识别的参数$μ$来推导$θ$的限制。例子包括在部分鉴定下的治疗选择和具有丰富未观察到的异质性的定价。我们的最优概念结合了一种最小值方法，可以从$μ$的$θ$的部分识别以及$μ$的平均风险最小化方法中处理歧义。我们在参数和半参数设置中使用Bootstrap和（Quasi-）贝叶斯方法来展示如何实现最佳决策规则。我们为治疗选择和最佳定价提供详细的应用。我们的渐近方法非常适合现实的经验环境，在这种情况下，有限样本最佳规则的推导是棘手的。
We derive asymptotically optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter $θ$ and the decision maker can use a point-identified parameter $μ$ to deduce restrictions on $θ$. Examples include treatment choice under partial identification and pricing with rich unobserved heterogeneity. Our notion of optimality combines a minimax approach to handle the ambiguity from partial identification of $θ$ given $μ$ with an average risk minimization approach for $μ$. We show how to implement optimal decision rules using the bootstrap and (quasi-)Bayesian methods in both parametric and semiparametric settings. We provide detailed applications to treatment choice and optimal pricing. Our asymptotic approach is well suited for realistic empirical settings in which the derivation of finite-sample optimal rules is intractable.
