Before revision:  To address this difficulty we propose two bootstrap methods that can consistently approximate the limit distribution : the gradient bootstrap and the multiplier bootstrap of the inverse propensity score weighted (IPW) estimator.
After revision:  To address this difficulty we propose two bootstrap methods that can consistently approximate the limit distribution of the original QTE estimator and lessen the burden of tuning parameter choice. Most especially, the multiplier bootstrap of the inverse propensity score weighted (IPW) estimator.