A doubly robust (DR) estimator is crucial in causal inference , which consists of two nuisance parameters : the conditional mean outcome and  logging policy (  probability of choosing an action)  . This paper provides a DR estimator for dependent samples obtained in adaptive experimentsand introduces two related topics. First, we propose adaptive-fitting as a variant of sample-splitting for showing an asymptotically normal semiparametric estimator from dependent samples without non-Donsker nuisance estimators . Second, we report an empirical paradox that a DR estimator shows better performances than other estimators using the true logging policy instead of its estimator . While a similar phenomenon is also known for estimators with i.i.d. samples, we hypothesize that traditional explanations based on asymptotic efficiency cannot elucidate our case with dependent samples. We confirm this hypothesis through simulation studies.
The doubly robust (DR) estimator , which consists of two nuisance parameters , the conditional mean outcome and the logging policy ( the probability of choosing an action) , is crucial in causal inference . This paper proposes a DR estimator for dependent samples obtained from adaptive experiments. To obtain an asymptotically normal semiparametric estimator from dependent samples with non-Donsker nuisance estimators , we propose adaptive-fitting as a variant of sample-splitting. We also report an empirical paradox that our proposed DR estimator tends to show better performances compared to other estimators utilizing the true logging policy . While a similar phenomenon is known for estimators with i.i.d. samples, traditional explanations based on asymptotic efficiency cannot elucidate our case with dependent samples. We confirm this hypothesis through simulation studies.
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