The quantification of treatment effects plays an important role in a wide range of applications, including policy making and bio-pharmaceutical research. In this article, we study the quantile treatment effect (QTE) while addressing two specific types of heterogeneities: (a) personalized heterogeneity, which captures the varying treatment effects for different individuals, and (b) quantile heterogeneity, which accounts for how the impact of covariates varies across different quantile levels. A well-designed debiased estimator for the individualized quantile treatment effect (IQTE) is proposed to capture such heterogeneities effectively. We show that this estimator converges weakly to a Gaussian process as a function of the quantile levels and propose valid statistical inference methods, including the construction of confidence intervals and the development of hypothesis testing decision rules. In addition, the minimax optimality frameworks for these inference procedures are established. Specifically, we derive the minimax optimal rates for the expected length of confidence intervals and the magnitude of the detection boundary for hypothesis testing procedures, illustrating the superiority of the proposed estimator. The effectiveness of our methods is demonstrated through extensive simulations and an analysis of the National Health and Nutrition Examination Survey (NHANES) datasets.

翻译：处理效应的量化在政策制定和生物医药研究等广泛领域中具有重要作用。本文研究分位数处理效应（QTE），同时解决两种特定类型的异质性：（a）个性化异质性，捕捉不同个体间变化的处理效应；（b）分位数异质性，解释协变量影响如何随不同分位数水平变化。我们提出了一种精心设计的针对个体化分位数处理效应（IQTE）的去偏估计量，以有效捕捉此类异质性。我们证明该估计量作为分位数水平的函数弱收敛于高斯过程，并提出了有效的统计推断方法，包括置信区间的构建和假设检验决策规则的开发。此外，我们建立了这些推断程序的极小极大最优性框架。具体而言，我们推导了置信区间期望长度的极小极大最优速率以及假设检验程序检测边界幅度的极小极大最优速率，从而证明了所提估计量的优越性。通过大量模拟实验和对国家健康与营养调查（NHANES）数据集的分析，验证了我们方法的有效性。