Efficient estimation under data fusion

Summary We aim to make inferences about a smooth, finite-dimensional parameter by fusing together data from multiple sources. Previous works have studied the estimation of variety parameters in similar fusion settings, including average treatment effect and reward under policy, with majority them merging one historical source covariates, actions rewards, same covariates. In this article, we consider general case where or more sources align each part distribution target population, such as conditional given describe potential gains efficiency that can arise these single analysis, which characterize reduction semiparametric bound. also provide means constructing estimators achieve bounds. Numerical simulations demonstrate marked improvements using proposed rather than their natural alternatives. Finally, illustrate magnitude be realized vaccine immunogenicity studies two HIV trials.