||Xinran Li, University of Pennsylvania
||Xiaojun Mao, School of Data Science, Fudan University
||15:00-16:00 Jan. 9, 2019
||Zibin N201, Fudan University
||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.
||Xinran Li is a postdoctoral researcher in the Department of Statistics at the University of Pennsylvania. He obtained his Ph.D. in Statistics from Harvard University in 2018, under the supervision of Jun S. Liu and Donald B. Rubin. Before that, He received his B.S. in Mathematics and Applied Mathematics from Peking University in 2013.