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February 2020 Rerandomization in $2^{K}$ factorial experiments
Xinran Li, Peng Ding, Donald B. Rubin
Ann. Statist. 48(1): 43-63 (February 2020). DOI: 10.1214/18-AOS1790

Abstract

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.

Citation

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Xinran Li. Peng Ding. Donald B. Rubin. "Rerandomization in $2^{K}$ factorial experiments." Ann. Statist. 48 (1) 43 - 63, February 2020. https://doi.org/10.1214/18-AOS1790

Information

Received: 1 September 2017; Revised: 1 September 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196529
MathSciNet: MR4065152
Digital Object Identifier: 10.1214/18-AOS1790

Subjects:
Primary: 62K10, 62K15
Secondary: 62K05

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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