Decision Theory for Treatment Choice Problems with Partial Identification
将经典统计决策理论应用于部分识别的治疗选择问题，发现所有决策规则都是可接受的，忽略数据是最大最小福利最优的，并刻画了最小化最大遗憾的决策规则。
Abstract We apply classical statistical decision theory to a large class of treatment choice problems with partial identification. We show that, in a general class of problems with Gaussian likelihood, all decision rules are admissible; it is maximin-welfare optimal to ignore all data; and, for severe enough partial identification, there are infinitely many minimax-regret optimal decision rules, all of which sometimes randomize the policy recommendation. We uniquely characterize the minimax-regret optimal rule that least frequently randomizes, and show that, in some cases, it can outperform other minimax-regret optimal rules in terms of what we call profiled regret. We analyse the implications of our results in the aggregation of experimental estimates for policy adoption, extrapolation of Local Average Treatment Effects, and policy making in the presence of omitted variable bias.