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Finely Stratified Rerandomization Designs

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  • Max Cytrynbaum

Abstract

We study estimation and inference on causal parameters under finely stratified rerandomization designs, which use baseline covariates to match units into groups (e.g. matched pairs), then rerandomize within-group treatment assignments until a balance criterion is satisfied. We show that finely stratified rerandomization does partially linear regression adjustment "by design," providing nonparametric control over the stratified covariates and linear control over the rerandomized covariates. We introduce several new rerandomization schemes, allowing for imbalance metrics based on nonlinear estimators. We also propose a novel minimax scheme that uses pilot data or prior information to minimize the computational cost of rerandomization, subject to a strict bound on statistical efficiency. While the asymptotic distribution of generalized method of moments (GMM) estimators under stratified rerandomization is generically non-normal, we show how to restore asymptotic normality using ex-post linear adjustment tailored to the stratification. This enables simple asymptotically exact inference on superpopulation parameters, as well as efficient conservative inference on finite population parameters.

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  • Max Cytrynbaum, 2024. "Finely Stratified Rerandomization Designs," Papers 2407.03279, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2407.03279
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    References listed on IDEAS

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    1. Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2018. "Inference Under Covariate-Adaptive Randomization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1784-1796, October.
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    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
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    5. Zhao, Anqi & Ding, Peng, 2024. "No star is good news: A unified look at rerandomization based on p-values from covariate balance tests," Journal of Econometrics, Elsevier, vol. 241(1).
    6. Yuehao Bai & Jizhou Liu & Azeem M. Shaikh & Max Tabord-Meehan, 2023. "On the Efficiency of Finely Stratified Experiments," Papers 2307.15181, arXiv.org, revised Aug 2024.
    7. Alberto Abadie & Guido W. Imbens, 2008. "Estimation of the Conditional Variance in Paired Experiments," Annals of Economics and Statistics, GENES, issue 91-92, pages 175-187.
    8. Max Cytrynbaum, 2023. "Covariate Adjustment in Stratified Experiments," Papers 2302.03687, arXiv.org, revised Jul 2024.
    9. Yuehao Bai, 2022. "Optimality of Matched-Pair Designs in Randomized Controlled Trials," American Economic Review, American Economic Association, vol. 112(12), pages 3911-3940, December.
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