  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.
