光华讲坛——社会名流与企业家论坛第 5200 期
主题：Rerandomization and ANCOVA
主办单位：统计研究中心 统计学院 科研处
Peng Ding received Ph.D. from the Harvard Statistics Department in May 2015 and worked as a postdoctoral researcher in the Harvard Epidemiology Department until December 2015. Since January 2016, he has been Assistant Professor in the Statistics Department of University of California, Berkeley. His research interests include causal inference, missing data, and experimental design.
Randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome-generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. R. A. Fisher suggested blocking on discrete covariates in the design stage or conducting the analysis of covariance (ANCOVA) in the analysis stage. In fact, we can embed blocking into a wider class of experimental design called rerandomization, and extend the classical ANCOVA to more general regression-adjusted estimators. Rerandomization trumps complete randomization in the design stage, and regression adjustment trumps the simple difference-in-means estimator in the analysis stage. It is then intuitive to use both rerandomization and regression adjustment. Under the randomization-inference framework, we establish a unified theory allowing the designer and analyzer to have access to different sets of covariates. We find that asymptotically (a) for any given estimator with or without regression adjustment, using rerandomization will never hurt either the sampling precision or the estimated precision, and (b) for any given design with or without rerandomization, using our regression-adjusted estimator will never hurt the estimated precision. Therefore, combining rerandomization and regression adjustment yields better coverage properties and thus improves causal inference. To theoretically quantify these statements, we first propose two notions of optimal regression-adjusted estimators, and then measure the additional gains of the designer and analyzer based on the sampling precision and estimated precision. This is a joint work with Xinran Li at Wharton.