The role of propensity score structure in asymptotic efficiency of estimated conditional quantile treatment effect

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