arXiv 10 Aug 2026 · Econometrics
arXiv:2608.09812 · PDF · Extracted main text
I study the optimal design and analysis of randomized experiments for estimating finite-population average treatment effects when potential outcomes are known to be bounded, as with binary outcomes. Among all assignment mechanisms and a broad class of affine estimators, worst-case mean-squared error (MSE) is minimized by independent random assignment and an unconventional regression of the support-midpoint-centered outcome on the recentered treatment, with no intercept. This contrasts with the usual prescription of balanced complete randomization and difference-in-means estimation: when outcomes are bounded, randomness in the realized treatment share is informative. The worst-case gain over full-sample complete randomization is asymptotically small, but gains can be first-order relative to other designs: complete within-pair randomization and pair-fixed-effect regression have twice the worst-case MSE. I extend the result to allow for arbitrary estimators. Independent random assignment remains optimal, and the generally-nonlinear optimal estimator can meaningfully reduce worst-case MSE.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hodges, J. L. and Lehmann, E. L (1982) Minimax Estimation in Simple Random Sampling | 0.843 | 4 | 3 | 75% |
| 2 | Bai, Yuehao (2023) Why Randomize? Minimax Optimality under Permutation Invariance | 0.511 | 2 | 1 | 100% |
| 3 | Borusyak, Kirill and Hull, Peter (2023) Nonrandom Exposure to Exogenous Shocks self | 0.511 | 2 | 1 | 100% |
| 4 | Borusyak, Kirill and Hull, Peter and Munro, Evan (2026) Robust Signal Maximization in Spillover Experiments self | 0.511 | 2 | 1 | 100% |
| 5 | Harshaw, Christopher and Sävje, Fredrik and Spielman, Daniel A. and… (2024) Balancing Covariates in Randomized Experiments with the Gram–Schmidt Walk Design | 0.511 | 2 | 1 | 100% |
| 6 | Kallus, Nathan (2021) On the Optimality of Randomization in Experimental Design: How to Randomize for Minimax Variance and Design-Based Inference | 0.511 | 2 | 1 | 100% |
| 7 | Aronow, Peter M. and Lopatto, Patrick (2026) Minimax Unbiased Estimation for Finite Populations with Bounded Outcomes | 0.405 | 1 | 1 | 100% |
| 8 | Bai, Yuehao (2022) Optimality of Matched-Pair Designs in Randomized Controlled Trials | 0.405 | 1 | 1 | 100% |
| 9 | Bickel, Peter J. and Herzberg, Agnes M (1979) Robustness of Design Against Autocorrelation in Time I: Asymptotic Theory, Optimality for Location and Linear Regression | 0.405 | 1 | 1 | 100% |
| 10 | Bickel, P. J. and Lehmann, E. L (1981) A Minimax Property of the Sample Mean in Finite Populations | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 23 scored citations.