Combining observational and experimental datasets using shrinkage estimators.

Area of Science:

• Causal inference
• Statistical modeling
• Data fusion

Background:

• Drawing causal conclusions from combined data sources is challenging.
• Existing methods may not fully leverage combined observational and experimental data.
• The Stein shrinkage literature provides a foundation for statistical estimation.

Purpose of the Study:

• To develop novel shrinkage estimators for combining observational and experimental data.
• To improve the accuracy and reliability of causal conclusions.
• To extend existing statistical methodologies for data fusion.

Main Methods:

• Extending results from the Stein shrinkage literature.
• Proposing a generic procedure for deriving shrinkage estimators using generalized unbiased risk estimation.
• Developing and analyzing two new estimators with finite sample and asymptotic properties.

Main Results:

• The proposed generic procedure facilitates the derivation of shrinkage estimators.
• Two new estimators demonstrate lower risk than using only experimental data under specific conditions.
• The new estimators achieve asymptotic optimality, enhancing causal inference.

Conclusions:

• The developed shrinkage estimators effectively combine observational and experimental data for causal inference.
• The approach offers improved statistical properties compared to using experimental data alone.
• Connections to sensitivity analysis are established, providing methods to evaluate estimator feasibility.