Optimal Experimental Design and Estimation when Potential Outcomes are Bounded

Peter Hull

Papers from arXiv.org

Abstract: 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.

Date: 2026-08, Revised 2026-08
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https://arxiv.org/pdf/2608.09812 Latest version (application/pdf)

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Working Paper: Optimal Experimental Design and Estimation when Potential Outcomes are Bounded (2026)
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