The role of propensity score in the efficient estimation of the average treatment effects is examined. If the treatment is ignorable given some observed characteristics, it is shown that the propensity score is ancillary for estimation of the average treatment effects but not for estimation of average treatment effects on the treated. Efficient semiparametric estimators take the form of relevant sample averages of the data completed by the nonparametric imputation method. Projection on the propensity score is not necessary for efficient semiparametric estimation of the average treatment effects on the treated even if the propensity score is known.

This paper introduces an alternative estimator for the linear censored quantile regression model. The estimator also applies to cases where the censoring point is unknown. Since the objective function is globally convex and the estimator is a solution to a linear programming problem, a global minimizer is obtained in a finite number of simplex iterations. The estimator has a square root of n-convergence rate and is asymptotically normal. A Monte Carlo study performed shows that the suggested estimator has very desirable small sample properties.