Timothy Sudijono, Edgar Dobriban, Eric Tchetgen Tchetgen
arXiv 13 Aug 2026 · Mathematics — Statistics Theory
arXiv:2608.13822 · PDF · Extracted main text
We study minimax-optimal designs and estimators for estimating the sample average treatment effect in finite population randomized experiments, where both design and estimator are unrestricted. For binary potential outcomes, we show this minimax risk is equivalent to the minimax risk $ρ_n^*$ of an estimation problem with $2$ unknown parameters. We leverage this reduction to establish a second-order risk expansion $ρ_n^* = n^{-1} - Cn^{-4/3} + o_n(n^{-4/3})$ for an explicit constant $C$ related to the Airy function. The minimax risk is attained by Bernoulli randomization with a nonlinear shrinkage estimator. Our results show that standard procedures such as complete randomization with difference in means are only minimax optimal up to first order in $n.$ We derive further results on admissibility of these procedures and discuss the practical implications of our results.
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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 | Imbens, Guido W and Rubin, Donald B (2015) Causal inference in statistics, social, and biomedical sciences | 1.000 | 5 | 3 | 100% |
| 2 | Ding, Peng (2024) A first course in causal inference | 0.843 | 3 | 3 | 100% |
| 3 | Kallus, Nathan (2018) Optimal a priori balance in the design of controlled experiments | 0.811 | 5 | 2 | 80% |
| 4 | Aronow, Peter M and Middleton, Joel A (2013) A class of unbiased estimators of the average treatment effect in randomized experiments | 0.811 | 4 | 2 | 100% |
| 5 | Aronow, PM and Lopatto, Patrick (2026) Minimax unbiased estimation for finite populations with bounded outcomes | 0.737 | 3 | 2 | 100% |
| 6 | Kandiros, Vardis and Harshaw, Christopher and Sävje, Fredrik (2026) A Design-Based Minimax Theory for Network Experiments | 0.693 | 5 | 1 | 100% |
| 7 | Kallus, Nathan (2021) On the optimality of randomization in experimental design: How to randomize for minimax variance and design-based inference | 0.644 | 4 | 1 | 100% |
| 8 | Bickel, Peter J (1981) Minimax estimation of the mean of a normal distribution when the parameter space is restricted | 0.644 | 2 | 2 | 100% |
| 9 | Johnstone, Iain M and MacGibbon, K Brenda (1992) Minimax estimation of a constrained Poisson vector | 0.644 | 2 | 2 | 100% |
| 10 | Levit, B Ya (1981) On asymptotic minimax estimates of the second order | 0.644 | 2 | 2 | 100% |
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