论文标题
关于实验设计中随机化的最佳性：如何随机化最小值差异和基于设计的推理
On the Optimality of Randomization in Experimental Design: How to Randomize for Minimax Variance and Design-Based Inference
论文作者
论文摘要
我研究了两臂对照实验的最小值 - 最佳设计，其中条件平均结果在给定的集合中可能有所不同。当该集合为对称性时，最佳设计是完全随机的，并且使用单个分区（即，仅将分区每一侧的治疗标签随机的设计随机设计）的最小值风险较大$ n-1 $。更一般而言，最佳设计被证明是Kallus（2018）的混合构成最佳设计（MSOD）。值得注意的是，即使一组条件均值结果具有结构（即不是置换对称），但对于方差而言，最小值 - 最佳选择仍然需要超越单个分区以外的随机化。尽管如此，由于这是针对精度的，因此它可能无法确保随机分组的足够均匀性，以通过Fisher的精确检验来实现随机分组（即基于设计的）推断，以适当检测到违规的侵犯。因此，我提出了推理约束的MSOD，在所有均匀性限制下，所有设计中都是最小的。在途中，我讨论了Johansson等人。 （2020年）最近比较了Morgan和Rubin（2012）的重读和Kallus（2018）的Pure-Strategy Optimal Design（PSOD）。我指出其中的一些错误，并直接设置了随机化是最小的，并且在Kallus（2018）中的“无免费午餐”定理和示例是正确的。
I study the minimax-optimal design for a two-arm controlled experiment where conditional mean outcomes may vary in a given set. When this set is permutation symmetric, the optimal design is complete randomization, and using a single partition (i.e., the design that only randomizes the treatment labels for each side of the partition) has minimax risk larger by a factor of $n-1$. More generally, the optimal design is shown to be the mixed-strategy optimal design (MSOD) of Kallus (2018). Notably, even when the set of conditional mean outcomes has structure (i.e., is not permutation symmetric), being minimax-optimal for variance still requires randomization beyond a single partition. Nonetheless, since this targets precision, it may still not ensure sufficient uniformity in randomization to enable randomization (i.e., design-based) inference by Fisher's exact test to appropriately detect violations of null. I therefore propose the inference-constrained MSOD, which is minimax-optimal among all designs subject to such uniformity constraints. On the way, I discuss Johansson et al. (2020) who recently compared rerandomization of Morgan and Rubin (2012) and the pure-strategy optimal design (PSOD) of Kallus (2018). I point out some errors therein and set straight that randomization is minimax-optimal and that the "no free lunch" theorem and example in Kallus (2018) are correct.
