SHARP BOUNDS ON THE DISTRIBUTION OF TREATMENT EFFECTS AND THEIR STATISTICAL INFERENCE
提出了二元处理效应分布尖锐界的非参数估计量，推导了其渐近分布，并采用少于n的bootstrap方法进行推断，通过模拟研究了不同置信区间的有限样本表现。
In this paper, we propose nonparametric estimators of sharp bounds on the distribution of treatment effects of a binary treatment and establish their asymptotic distributions. We note the possible failure of the standard bootstrap with the same sample size and apply the fewer-than- n bootstrap to making inferences on these bounds. The finite sample performances of the confidence intervals for the bounds based on normal critical values, the standard bootstrap, and the fewer-than- n bootstrap are investigated via a simulation study. Finally we establish sharp bounds on the treatment effect distribution when covariates are available.