When a strict subset of covariates is given, we propose conditional quantile treatment effect ($CQTE$𝐶𝑄𝑇𝐸$CQTE$) to offer, compared with the unconditional quantile treatment effect ($QTE$𝑄𝑇𝐸$QTE$) and conditional average treatment effect ($CATE$𝐶𝐴𝑇𝐸$CATE$), a more complete and informative view of the heterogeneity of treatment effects via the quantile sheet that is a function of the given covariates and quantile levels. Even though either one or both $QTE$𝑄𝑇𝐸$QTE$ and $CATE$𝐶𝐴𝑇𝐸$CATE$ are not significant, $CQTE$𝐶𝑄𝑇𝐸$CQTE$ could still show some impact of the treatment on the upper and lower tails of subpopulations' (defined by the covariates subset) distribution. To the best of our knowledge, this is the first to consider such a low-dimensional conditional quantile treatment effect in the literature. We focus on deriving the asymptotic normality of propensity score-based estimators under parametric, nonparametric, and semiparametric structure. We make a systematic study on the estimation efficiency to check the importance of propensity score structure and the essential differences from the unconditional counterparts. The derived unique properties can answer: what is the general ranking of these estimators? how does the affiliation of the given covariates to the set of covariates of the propensity score affect the efficiency? how does the convergence rate of the estimated propensity score affect the efficiency? and why would semiparametric estimation be worth of recommendation in practice? The simulation studies are conducted to examine the performances of these estimators. A real data example is analyzed for illustration and some new findings are acquired.

中文翻译：

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倾向得分结构在估计条件分位数处理效果的渐近效率中的作用

当给定一个严格的协变量子集时，我们提出条件分位数处理效果（$C问吨乙$𝐶𝑄𝑇 _𝐸$CQTE$) 提供，与无条件分位数处理效果相比 ($问吨乙$𝑄𝑇 _𝐸$QTE$) 和条件平均处理效果 ($C\mathrm{一种}吨乙$𝐶𝐴𝑇 _𝐸$CATE$)，通过作为给定协变量和分位数水平的函数的分位数表对治疗效果的异质性进行更完整和信息丰富的视图。即使其中之一或两者$问吨乙$𝑄𝑇 _𝐸$QTE$和$C\mathrm{一种}吨乙$𝐶𝐴𝑇 _𝐸$CATE$不显着，$C问吨乙$𝐶𝑄𝑇 _𝐸$CQTE$仍然可以显示处理对亚群（由协变量子集定义）分布的上尾和下尾的一些影响。据我们所知，这是文献中首次考虑这种低维条件分位数处理效果。我们专注于在参数、非参数和半参数结构下推导基于倾向得分的估计量的渐近正态性。我们对估计效率进行了系统研究，以检查倾向得分结构的重要性以及与无条件对应项的本质区别。派生的独特属性可以回答：这些估计器的一般排名是什么？给定协变量与倾向得分协变量集的关联如何影响效率？估计倾向得分的收敛速度如何影响效率？为什么半参数估计在实践中值得推荐？进行模拟研究以检查这些估计器的性能。为了说明，分析了一个真实的数据示例，并获得了一些新的发现。