Motivated by the proliferation of observational datasets and the need to integrate non-randomized evidence with randomized controlled trials, causal inference researchers have recently proposed several new methodologies for combining biased and unbiased estimators. We contribute to this growing literature by developing a new class of estimators for the data-combination problem: double-shrinkage estimators. Double-shrinkers first compute a data-driven convex combination of the the biased and unbiased estimators, and then apply a final, Stein-like shrinkage toward zero. Such estimators do not require hyperparameter tuning, and are targeted at multidimensional causal estimands, such as vectors of conditional average treatment effects (CATEs). We derive several workable versions of double-shrinkage estimators and propose a method for constructing valid Empirical Bayes confidence intervals. We also demonstrate the utility of our estimators using simulations on data from the Women's Health Initiative.

翻译：受观测数据集激增以及将非随机化证据与随机对照试验相结合的迫切需求驱动，因果推断研究者近年来提出了一系列融合有偏与无偏估计量的新方法。本文通过发展一类新的数据融合估计量——双重收缩估计量——为该新兴领域做出贡献。双重收缩估计首先计算有偏与无偏估计量的数据驱动凸组合，随后对组合结果施加类Stein型收缩至零的最终处理。该类估计量无需超参数调优，专门针对多维因果参数（如条件平均处理效应向量）设计。我们推导出双重收缩估计量的若干可行变体，并提出了构建有效经验贝叶斯置信区间的方法。最后，通过基于妇女健康倡议数据的模拟实验验证了所提估计量的实用性。