Rerandomization and regression adjustment
By Xinran Li, Peng Ding. Journal of The Royal Statistical Society Series B-statistical Methodology, 2019
115 citations recorded by the source corpus.
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 analysis of covariance in the analysis stage. We can embed blocking in a wider class of experimental design called rerandomization, and extend the classical analysis of covariance to more general regression adjustment. 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 analyser to have access to different sets of covariates. We find that asymptotically, for any given estimator with or without regression adjustment, rerandomization never hurts either the sampling precision or the estimated precision, and, for any given design with or without rerandomization, our regression‐adjusted estimator never hurts the estimated precision. Therefore, combining rerandomization and regression adjustment yields better coverage properties and thus improves statistical inference. To quantify these statements theoretically, we discuss optimal regression‐adjusted estimators in terms of the sampling precision and the estimated precision, and then measure the additional gains of the designer and the analyser. We finally suggest the use of rerandomization in the design and regression adjustment in the analysis followed by the Huber–White robust standard error.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/692deded02a915cd71b63e9fb044e1f996795caa
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Citations in the corpus
- The Generalized Oaxaca-Blinder Estimator (2020, methodology): “Like the results of prior work on covariate adjustment with linear models (Bloniarz et al. 2016; Fogarty 2018; Freedman 2008a,b; Li and Ding 2020; Liu and Yang 2020), our theoretical guarantees are asymptotic.”
- Covariate-adjusted Fisher randomization tests for the average treatment effect (2020, methodology): “al concern in practice, is what if the designer and the analyzer do not communicate? Bruhn and McKenzie (2009) and Heckman and Karapakula (2019) gave examples arising in eld experiments in economics; Li and Ding (2020) discussed optimal covariate adjustment based on estimation precision. A relativel”