This was part of Permutation and Causal Inference
Berry-Esseen bounds for design-based causal inference with possibly diverging treatment levels and varying group sizes
Lei Shi, University of California, Berkeley
Thursday, August 24, 2023
Abstract: 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 varies. 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 permutational 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 basis for design-based causal inference with possibly diverging treatment levels and a diverging number of contrasts. 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.