Understanding the Risks and Rewards of Combining Unbiased and Possibly Biased Estimators, with Applications to Causal Inference
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组合无偏与可能有偏估计量的风险和收益：因果推断应用
- 研究问题
- 研究如何组合高方差无偏估计量与低方差但可能有偏的估计量，并评估未知偏差下有限样本误差的收益与风险。
- 方法与思路
- 作者以误差随未知偏差变化的曲线及偏差阈值比较既有方法，提出替代组合方法，并推导依赖方差和协方差的均方误差界。
- 材料陈述的贡献
- 摘要称，新方法在模拟中具有较高偏差阈值、较保守的最佳与最差情形权衡，并给出适用于任意未知偏差大小的误差界。
- 阅读关注点
- 应核对组合估计量的公式、偏差阈值定义、均方误差界的前提，以及实验与观察估计量之间的相关性如何处理。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未给出误差界公式或模拟细节，所述比较优势不能外推至所有情形。
原文摘要
Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining small experimental datasets with larger observational datasets. There exist a series of recent proposals on how to perform such a combination, even when the bias of the low-variance estimator is unknown. To build intuition for the differing trade-offs of competing approaches, we argue for examining the finite-sample estimation error of each approach as a function of the unknown bias. This includes understanding the bias threshold -- the largest bias for which a given approach improves over using the unbiased estimator alone. Though this lens, we review several recent proposals, and observe in simulation that different approaches exhibits qualitatively different behavior. We also introduce a simple alternative approach, which compares favorably in simulation to recent alternatives, having a higher bias threshold and generally making a more conservative trade-off between best-case performance (when the bias is zero) and worst-case performance (when the bias is adversarially chosen). More broadly, we prove that for any amount of (unknown) bias, the MSE of this estimator can be bounded in a transparent way that depends on the variance / covariance of the underlying estimators that are being combined.