Optimal Decision Rules When Payoffs are Partially Identified
研究了当收益依赖于部分可识别的参数时，如何构造渐近最优的统计决策规则，结合极小极大和平均风险最小化方法，适用于处理选择与定价问题。
Abstract 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.