We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the corresponding central-limit-theorem-based confidence intervals by a factor depending on the square root of the propensity score. We show that this performance gap can be closed, designing nonasymptotic confidence intervals that have the same effective sample size as their asymptotic counterparts. Our approach involves systematic exploitation of negative dependence or variance adaptivity (or both). We also show that the nonasymptotic rates that we achieve are unimprovable in an information-theoretic sense.

翻译：本文研究随机化实验中处理效应的非渐近（有限样本）置信区间。现有文献中，非渐近置信区间的有效样本量往往比基于中心极限定理的对应置信区间宽松一个与倾向得分平方根相关的因子。我们证明这一性能差距可以被消除，通过设计具有与渐近对应区间相同有效样本量的非渐近置信区间。我们的方法系统性地利用了负相关性或方差自适应性（或两者兼具）。我们还证明，所实现的非渐近速率在信息论意义上是不可改进的。