Neyman[106]'s seminal work in 1923 has been a milestone in statistics over the century, which has motivated many fundamental statistical concepts and methodology. In this review, we delve into Neyman[106]'s groundbreaking contribution and offer technical insights into the design and analysis of randomized experiments. We shall review the basic setup of completely randomized experiments and the classical approaches for inferring the average treatment effects. We shall in particular review more efficient design and analysis of randomized experiments by utilizing pretreatment covariates, which move beyond Neyman's original work without involving any covariate. We then summarize several technical ingredients regarding randomizations and permutations that have been developed over the century, such as permutational central limit theorems and Berry-Esseen bounds, and elaborate on how these technical results facilitate the understanding of randomized experiments. The discussion is also extended to other randomized experiments including rerandomization, stratified randomized experiments, matched pair experiments, cluster randomized experiments, etc.

翻译：Neyman[106]于1923年的开创性工作已成为统计学领域一个世纪以来的里程碑，其启发了许多基础统计概念与方法论。本综述深入探讨Neyman[106]的突破性贡献，并对随机实验的设计与分析提供技术性见解。我们将回顾完全随机实验的基本框架及推断平均处理效应的经典方法，特别重点评述利用预处理协变量实现更高效的随机实验设计与分析——这些方法超越了Neyman最初未涉及任何协变量的研究框架。随后，我们总结近百年来发展形成的关于随机化与置换的若干技术要素，如置换中心极限定理与Berry-Esseen界，并阐述这些技术成果如何深化对随机实验的理解。讨论范围还延伸至其他随机实验类型，包括再随机化、分层随机实验、配对实验、整群随机实验等。