We propose a new procedure for inference on optimal treatment regimes in the model-free setting, which does not require to specify an outcome regression model. Existing model-free estimators for optimal treatment regimes are usually not suitable for the purpose of inference, because they either have nonstandard asymptotic distributions or do not necessarily guarantee consistent estimation of the parameter indexing the Bayes rule due to the use of surrogate loss. We first study a smoothed robust estimator that directly targets the parameter corresponding to the Bayes decision rule for optimal treatment regimes estimation. This estimator is shown to have an asymptotic normal distribution. Furthermore, we verify that a resampling procedure provides asymptotically accurate inference for both the parameter indexing the optimal treatment regime and the optimal value function. A new algorithm is developed to calculate the proposed estimator with substantially improved speed and stability. Numerical results demonstrate the satisfactory performance of the new methods.

中文翻译：

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基于重采样的置信区间对最佳治疗方案的无模型鲁棒推断

我们提出了一种在无模型设置中推断最佳治疗方案的新程序，它不需要指定结果回归模型。现有的最佳治疗方案的无模型估计量通常不适合推理的目的，因为它们要么具有非标准渐近分布，要么由于使用代理损失而不一定保证索引贝叶斯规则的参数的一致估计。我们首先研究了一个平滑的稳健估计器，它直接针对与贝叶斯决策规则相对应的参数，以进行最佳治疗方案估计。该估计量显示为具有渐近正态分布。此外，我们验证了重采样过程为索引最佳治疗方案和最佳价值函数的参数提供了渐近准确的推断。开发了一种新算法来计算建议的估计量，其速度和稳定性都得到了显着提高。数值结果证明了新方法的令人满意的性能。