  In this paper the estimation of the distribution function for potential
outcomes to receiving or not receiving a treatment is studied. The approach is
based on weighting observed data on the basis on estimated propensity score. A
weighted version of empirical process is constructed and its weak convergence
to bivariate Gaussian process is established. Results for the estimation of the
Average Treatment Effect (ATE) and Quantile Treatment Effect (QTE) are obtained
as by-products. Applications to the construction of nonparametric tests for the
treatment effect and for the stochastic dominance of the treatment over control
are considered, and their finite sample properties and merits are studied via
simulation.
