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Improved methods for moment restriction models with data combination and an application to two‐sample instrumental variable estimation
The Canadian Journal of Statistics ( IF 0.8 ) Pub Date : 2019-12-26 , DOI: 10.1002/cjs.11530
Heng Shu 1 , Zhiqiang Tan 2
Affiliation  

Combining‐100 information from multiple samples is often needed in biomedical and economic studies, but differences between these samples must be appropriately taken into account in the analysis of the combined data. We study the estimation for moment restriction models with data combined from two samples under an ignorability‐type assumption while allowing for different marginal distributions of variables common to both samples. Suppose that an outcome regression (OR) model and a propensity score (PS) model are specified. By leveraging semi‐parametric efficiency theory, we derive an augmented inverse probability‐weighted (AIPW) estimator that is locally efficient and doubly robust with respect to these models. Furthermore, we develop calibrated regression and likelihood estimators that are not only locally efficient and doubly robust but also intrinsically efficient in achieving smaller variances than the AIPW estimator when the PS model is correctly specified but the OR model may be mispecified. As an important application, we study the two‐sample instrumental variable problem and derive the corresponding estimators while allowing for incompatible distributions of variables common to the two samples. Finally, we provide a simulation study and an econometric application on public housing projects to demonstrate the superior performance of our improved estimators. The Canadian Journal of Statistics 48: 259–284; 2020 © 2019 Statistical Society of Canada

中文翻译:

具有数据组合的力矩限制模型的改进方法及其在两样本工具变量估计中的应用

在生物医学和经济研究中,经常需要将多个样本中的100个信息组合在一起,但是在分析组合数据时必须适当考虑这些样本之间的差异。我们使用可忽略性类型的假设,结合两个样本的数据,研究了力矩限制模型的估计,同时考虑了两个样本共有的变量的不同边际分布。假设指定了结果回归(OR)模型和倾向得分(PS)模型。通过利用半参数效率理论,我们得出了一个增强的逆概率加权(AIPW)估计量,该估计量在局部效率方面相对于这些模型具有双重健壮性。此外,我们开发了经过校准的回归和似然估计器,它们不仅局部有效且具有双重鲁棒性,而且在正确指定PS模型但可能会指定OR模型时,在实现比AIPW估计器小的方差方面具有内在效率。作为一个重要的应用程序,我们研究了两个样本的工具变量问题,并推导了相应的估计量,同时允许两个样本共有的变量的分布不兼容。最后,我们在公共住房项目上提供了模拟研究和计量经济学应用,以证明我们改进的估算器的卓越性能。我们研究了两个样本的工具变量问题,并推导了相应的估计量,同时允许两个样本共有的变量的分布不兼容。最后,我们在公共住房项目上提供了模拟研究和计量经济学应用,以证明我们改进的估算器的卓越性能。我们研究了两个样本的工具变量问题,并推导了相应的估计量,同时允许两个样本共有的变量的分布不兼容。最后,我们在公共住房项目上提供了模拟研究和计量经济学应用,以证明我们改进的估算器的卓越性能。加拿大统计杂志48:259–284;加拿大统计局。2020©2019加拿大统计学会
更新日期:2019-12-26
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