Resampling-based Confidence Intervals for Model-free Robust Inference on Optimal Treatment Regimes
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Recently, there has been growing interest in estimating optimal treatment regimes which are individualized decision rules that can achieve maximal average outcomes. This paper considers the problem of inference for optimal treatment regimes in the model-free setting, where the specification of an outcome regression model is not needed. Existing model-free estimators are usually not suitable for the purpose of inference because they either have nonstandard asymptotic distributions, or are designed to achieve fisher-consistent classification performance. This paper first studies a smoothed robust estimator that directly targets estimating the parameters corresponding to the Bayes decision rule for estimating the optimal treatment regime. This estimator is shown to have an asymptotic normal distribution. Furthermore, it is proved that a resampling procedure provides asymptotically accurate inference for both the parameters 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.
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