Efficient data fusion under exchangeability of functionals

Thomas M. Menino Convention & Exhibition Center 

We study estimation and inference for a finite-dimensional parameter by integrating multiple heterogeneous data sources. Prior data fusion works typically assume that source distributions fully or weakly align with the target distribution via shared conditional distributions that are exchangeable or differ up to an unknown finite-dimensional parameter. However, in many applications source data heterogeneity exceeds these alignment regimes. In this work, we consider efficient estimation under data fusion when some, possibly infinite-dimensional, functionals are exchangeable between the target and source distributions. In this setting, we derive the semiparametric efficiency bound and characterize the efficiency gain by integrating heterogeneous source data. We also provide a general construction of efficient estimators that uses all available data and leverages flexible machine-learning methods. We illustrate our theoretical results with the example of estimating average treatment effect with external controls. We also demonstrate the performance of the proposed estimator via simulation studies.

Data fusion

semiparametric efficiency

debiased machine learning

causal inference 

Biometrics Section