Rerandomization in 2K factorial experiments

Xinran Li, Peng Ding, Donald B. Rubin

Research output: Contribution to journalArticlepeer-review


With many pretreatment covariates and treatment factors, the classical factorial experiment often fails to balance covariates across multiple factorial effects simultaneously. Therefore, it is intuitive to restrict the randomization of the treatment factors to satisfy certain covariate balance criteria, possibly conforming to the tiers of factorial effects and covariates based on their relative importances. This is rerandomization in factorial experiments. We study the asymptotic properties of this experimental design under the randomization inference framework without imposing any distributional or modeling assumptions of the covariates and outcomes. We derive the joint asymptotic sampling distribution of the usual estimators of the factorial effects, and show that it is symmetric, unimodal and more “concentrated” at the true factorial effects under rerandomization than under the classical factorial experiment. We quantify this advantage of rerandomization using the notions of “central convex unimodality” and “peakedness” of the joint asymptotic sampling distribution. We also construct conservative large-sample confidence sets for the factorial effects.

Original languageEnglish (US)
Pages (from-to)43-63
Number of pages21
JournalAnnals of Statistics
Issue number1
StatePublished - 2020
Externally publishedYes


  • Covariate balance
  • Tiers of covariates
  • Tiers of factorial effects

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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