RERANDOMIZATION IN 2K FACTORIAL EXPERIMENTS

• 成果类型: Article
• 署名作者: Li, Xinran; Ding, Peng; Rubin, Donald B.
• 署名单位: University of Pennsylvania; University of California System; University of California Berkeley; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1790
• 发表日期: 2020
• 页码: 43-63
• 关键词: covariate balance; randomization; DESIGN

摘要

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.