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

• 成果类型: Editorial Material
• 署名作者: Kallus, Nathan
• 署名单位: Cornell University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12412
• 发表日期: 2021
• 页码: 404-409
• 关键词: balance

摘要

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.