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. 2023 Dec;79(4):2961-2973.
doi: 10.1111/biom.13827. Epub 2023 Jan 27.

Combining observational and experimental datasets using shrinkage estimators

Evan T R Rosenman  1 , Guillaume Basse  2 , Art B Owen  3 , Mike Baiocchi  3
Affiliations

Combining observational and experimental datasets using shrinkage estimators

Evan T R Rosenman et al. Biometrics. 2023 Dec.

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.

Keywords: causal inference; data fusion; sensitivity analysis; shrinkage.

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References

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