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Combining observational and experimental datasets using shrinkage estimators

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  • Evan T.R. Rosenman
  • Guillaume Basse
  • Art B. Owen
  • Mike Baiocchi

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.

Suggested Citation

  • Evan T.R. Rosenman & Guillaume Basse & Art B. Owen & Mike Baiocchi, 2023. "Combining observational and experimental datasets using shrinkage estimators," Biometrics, The International Biometric Society, vol. 79(4), pages 2961-2973, December.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:2961-2973
    DOI: 10.1111/biom.13827
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    References listed on IDEAS

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    Cited by:

    1. Irina Degtiar & Tim Layton & Jacob Wallace & Sherri Rose, 2023. "Conditional cross‐design synthesis estimators for generalizability in Medicaid," Biometrics, The International Biometric Society, vol. 79(4), pages 3859-3872, December.

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