This paper establishes a combinatorial central limit theorem for stratified randomization that holds under Lindeberg-type conditions and allows for a growing number of large and small strata. The result is then applied to derive the asymptotic distributions of two test statistics proposed in a finite population setting with randomly assigned instruments and a super population instrumental variables model, both having many strata.

翻译：本文建立了分层随机化的组合中心极限定理，该定理在满足Lindeberg型条件下成立，并允许大、小层的数量不断增加。随后，将该结果应用于推导两种检验统计量的渐近分布：一是在有限总体设定下使用随机分配的工具变量，二是在具有超总体工具变量模型且两者均包含大量分层的情形。