Berry–Esseen bounds for design-based causal inference with possibly diverging treatment levels and varying group sizes
本文在Neyman随机化模型下，针对处理水平数发散且组大小变化的情形，推导了估计量的Berry-Esseen界，并提出了无重复实验的方差估计量，为基于设计的因果推断提供了更强的理论保证。
Neyman (1923/1990) introduced the randomization model, which contains the notation of potential outcomes to define causal effects and a framework for large-sample inference based on the design of the experiment. However, the existing theory for this framework is far from complete, especially when the number of treatment levels diverges and the treatment group sizes vary. We provide a unified discussion of statistical inference under the randomization model with general treatment group sizes. We formulate the estimator in terms of a linear permutation statistic and use results based on Stein’s method to derive various Berry–Esseen bounds on the linear and quadratic functions of the estimator. These new Berry–Esseen bounds serve as the basis for design-based causal inference with possibly diverging treatment levels and a diverging number of causal parameters of interest. We also fill an important gap by proposing novel variance estimators for experiments with possibly many treatment levels without replications. Equipped with the newly developed results, design-based causal inference in general settings becomes more convenient with stronger theoretical guarantees.