Balancing Covariates in Randomized Experiments with the Gram–Schmidt Walk Design
Name
Balancing Covariates in Randomized Experiments with the Gram Schmidt Walk Design.pdf
Description
Published version
Size
1.78 MB
Format
Adobe PDF
Checksum (MD5)
93651a49627936bda1fbaed128373884
Author(s)
Harshaw, Christopher
Sävje, Fredrik
Spielman, Daniel A
Zhang, Peng
Date Issued
October 1, 2024
Journal
Journal of the American Statistical Association
Publisher
Taylor & Francis
Citation
Harshaw, C., Sävje, F., Spielman, D. A., & Zhang, P. (2024). Balancing Covariates in Randomized Experiments with the Gram–Schmidt Walk Design. Journal of the American Statistical Association, 119(548), 2934–2946.
Version
Final published version
Abstract
The design of experiments involves a compromise between covariate balance and robustness. This article provides a formalization of this tradeoff and describes an experimental design that allows experimenters to navigate it. The design is specified by a robustness parameter that bounds the worst-case mean squared error of an estimator of the average treatment effect. Subject to the experimenter’s desired level of robustness, the design aims to simultaneously balance all linear functions of potentially many covariates. Less robustness allows for more balance. We show that the mean squared error of the estimator is bounded in finite samples by the minimum of the loss function of an implicit ridge regression of the potential outcomes on the covariates. Asymptotically, the design perfectly balances all linear functions of a growing number of covariates with a diminishing reduction in robustness, effectively allowing experimenters to escape the compromise between balance and robustness in large samples. Finally, we describe conditions that ensure asymptotic normality and provide a conservative variance estimator, which facilitate the construction of asymptotically valid confidence intervals. Supplementary materials for this article are available online.
MIT Department
MIT Open Learning
Statistics and Data Science Center (Massachusetts Institute of Technology)
Terms of Use
Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1080/01621459.2023.2285474
