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On the optimality of randomization in experimental design: How to randomize for minimax variance and design‐based inference

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  • Nathan Kallus

Abstract

I study the minimax‐optimal design for a two‐arm controlled experiment where conditional mean outcomes vary in a given set and the objective is effect‐estimation precision. When this set is permutation symmetric, the optimal design is shown to be complete randomization. Notably, even when the set has structure (i.e., is not permutation symmetric), being minimax‐optimal for precision still requires randomization beyond a single partition of units, that is, beyond randomizing the identity of treatment. A single partition is not optimal even when conditional means are linear. Since this only targets precision, it may nonetheless not ensure sufficient uniformity for design‐based (i.e., randomization) inference. I therefore propose the inference‐constrained mixed‐strategy optimal design as the minimax‐optimal for precision among designs subject to sufficient‐uniformity constraints.

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  • Nathan Kallus, 2021. "On the optimality of randomization in experimental design: How to randomize for minimax variance and design‐based inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 404-409, April.
    • Handle: RePEc:bla:jorssb:v:83:y:2021:i:2:p:404-409
    DOI: 10.1111/rssb.12412
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    References listed on IDEAS

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    1. Per Johansson & Donald B. Rubin & Mårten Schultzberg, 2021. "On optimal rerandomization designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 395-403, April.
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    Cited by:

    1. Belmiro P. M. Duarte & Anthony C. Atkinson & David Pedrosa & Marlena van Munster, 2024. "Compound Optimum Designs for Clinical Trials in Personalized Medicine," Mathematics, MDPI, vol. 12(19), pages 1-20, September.
    2. Yuchen Hu & Henry Zhu & Emma Brunskill & Stefan Wager, 2024. "Minimax-Regret Sample Selection in Randomized Experiments," Papers 2403.01386, arXiv.org, revised Jun 2024.
    3. Yuehao Bai & Azeem M. Shaikh & Max Tabord-Meehan, 2024. "A Primer on the Analysis of Randomized Experiments and a Survey of some Recent Advances," Papers 2405.03910, arXiv.org.
    4. Bai, Yuehao, 2023. "Why randomize? Minimax optimality under permutation invariance," Journal of Econometrics, Elsevier, vol. 232(2), pages 565-575.

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