Before revision:  The proposed adaptive DR estimator only requires the convergence rate conditions of the nuisance estimators and the other mild regularity conditions; that is, we do not impose a specific time-series structure and Donsker's condition. We investigate the effectiveness by using benchmark datasets compared to a past proposed DR estimator with double/debiased machine learning and an adaptive version of an augmented IPW estimator .
After revision:  We first summarize existing and new theoretical results for such OPE estimators. Then, we compare their empirical properties using benchmark datasets compared to a past proposed DR estimator with double/debiased machine learning and an adaptive version of an augmented IPW estimator .