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Abstract:
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We aim to make inferences about a smooth finite-dimensional parameter by fusing data from multiple sources together. Previous works have studied the estimation of a variety of parameters in similar data fusion settings, including the average treatment effect, optimal treatment rule, or average reward, with the majority of them merging one historical dataset with covariates, actions, and rewards and one dataset of the same covariates. In this work, we consider the general case where multiple datasets align with different parts of the distribution of the target population, for example, the conditional distribution of the reward given actions and covariates. We then examine potential gains in efficiency that can arise from fusing these datasets together in a single analysis, which are characterized by a reduction in the semiparametric efficiency bound. Our framework allows researchers to tackle data fusion problems in generality without limiting themselves to specific parameters, numbers of data sources, or particular data structures. In a variety of examples, we show marked improvements in efficiency from using our proposed estimators compared to natural alternatives.
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