Combining Observational and Experimental Datasets Using Shrinkage Estimators
Abstract
We consider the problem of combining data from observational and experimental sources to draw causal conclusions. To derive combined estimators with desirable properties, we extend results from the Stein shrinkage literature. Our contributions are threefold. First, we propose a generic procedure for deriving shrinkage estimators in this setting, making use of a generalized unbiased risk estimate. Second, we develop two new estimators, prove finite sample conditions under which they have lower risk than an estimator using only experimental data, and show that each achieves a notion of asymptotic optimality. Third, we draw connections between our approach and results in sensitivity analysis, including proposing a method for evaluating the feasibility of our estimators.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 11, 2023
- Source ID
- 10.1111/biom.13827
Entities
People
- Art B. Owen
- Evan Rosenman
- Guillaume Basse
- Mike Baiocchi
Organizations
- Citadel Enterprise Americas LLC
- Harvard University
- National Natural Science Foundation of China
- National Science Foundation
- Stanford University
- United States Department of Defense