Nonparametric bootstrap for propensity score matching estimators

We introduce and prove the validity of nonparametric bootstrap procedures for the approximation of the sampling distribution of pair or one -to -many propensity score matching estimators. Unlike the conventional bootstrap, the proposed bootstrap approach does not construct bootstrap samples by randomly resampling from the observations with uniform weights. Instead, it constructs the bootstrap approximation by randomly resampling from the martingale representation for matching estimators. Finally, we also conduct a simulation study in which the nonparametric bootstrap performs well even when the sample size is relatively small.