With the increasing availability of datasets, developing data fusion methods to leverage the strengths of different datasets to draw causal effects is of great practical importance to many scientific fields. In this paper, we consider estimating the quantile treatment effects using small validation data with fully-observed confounders and large auxiliary data with unmeasured confounders. We propose a Fused Quantile Treatment effects Estimator (FQTE) by integrating the information from two datasets based on doubly robust estimating functions. We allow for the misspecification of the models on the dataset with unmeasured confounders. Under mild conditions, we show that the proposed FQTE is asymptotically normal and more efficient than the initial QTE estimator using the validation data solely. By establishing the asymptotic linear forms of related estimators, convenient methods for covariance estimation are provided. Simulation studies demonstrate the empirical validity and improved efficiency of our fused estimators. We illustrate the proposed method with an application.

翻译：随着数据集的日益丰富，开发数据融合方法以利用不同数据集的优势推断因果效应，对众多科学领域具有重要的实际意义。本文考虑利用含有完全观测混杂因素的小规模验证数据与含有未观测混杂因素的大规模辅助数据，估计分位数处理效应。我们基于双重稳健估计函数，提出了一种融合分位数处理效应估计器（Fused Quantile Treatment effects Estimator，FQTE），用以整合两个数据集的信息。我们允许包含未观测混杂因素的数据集上的模型存在设定错误。在温和条件下，研究表明，所提出的FQTE具有渐近正态性，且相较于仅使用验证数据的初始QTE估计器更为高效。通过建立相关估计量的渐近线性形式，我们提供了协方差估计的便捷方法。仿真实验验证了所提融合估计器的实证有效性与效率提升。最后，我们通过一项实际应用对所提方法进行说明。