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On optimal rerandomization designs
The Journal of the Royal Statistical Society, Series B (Statistical Methodology) ( IF 5.8 ) Pub Date : 2021-03-23 , DOI: 10.1111/rssb.12417 Per Johansson 1, 2 , Donald B. Rubin 2 , Mårten Schultzberg 3
The Journal of the Royal Statistical Society, Series B (Statistical Methodology) ( IF 5.8 ) Pub Date : 2021-03-23 , DOI: 10.1111/rssb.12417 Per Johansson 1, 2 , Donald B. Rubin 2 , Mårten Schultzberg 3
Affiliation
Blocking is commonly used in randomized experiments to increase efficiency of estimation. A generalization of blocking removes allocations with imbalance in covariate distributions between treated and control units, and then randomizes within the remaining set of allocations with balance. This idea of rerandomization was formalized by Morgan and Rubin (Annals of Statistics, 2012, 40, 1263–1282), who suggested using Mahalanobis distance between treated and control covariate means as the criterion for removing unbalanced allocations. Kallus (Journal of the Royal Statistical Society, Series B: Statistical Methodology, 2018, 80, 85–112) proposed reducing the set of balanced allocations to the minimum. Here we discuss the implication of such an ‘optimal’ rerandomization design for inferences to the units in the sample and to the population from which the units in the sample were randomly drawn. We argue that, in general, it is a bad idea to seek the optimal design for an inference because that inference typically only reflects uncertainty from the random sampling of units, which is usually hypothetical, and not the randomization of units to treatment versus control.
中文翻译:
关于最佳的重新随机化设计
分组通常用于随机实验中,以提高估计效率。阻塞的一般化将删除处理单元和控制单元之间协变量分布不平衡的分配,然后在其余的平衡分配集中进行随机化。的这个想法rerandomization由摩根和Rubin(形式化统计年鉴,2012年,40,1263年至1282年),使用处理的和对照的协变量装置作为标准来去除不平衡分配之间的马氏距离谁建议。Kallus(皇家统计学会,B系列:统计方法,2018年,80(85-112)建议将平衡分配的集合减少到最小。在这里,我们讨论了这种“最佳”重新随机化设计的含义,以推断样本中的单位以及样本中的单位是从中随机抽取的总体。我们认为,总的来说,为推论寻求最佳设计是个坏主意,因为推论通常仅反映单位随机抽样的不确定性(通常是假设的),而不是单位随机分配给治疗与对照。
更新日期:2021-04-15
中文翻译:
关于最佳的重新随机化设计
分组通常用于随机实验中,以提高估计效率。阻塞的一般化将删除处理单元和控制单元之间协变量分布不平衡的分配,然后在其余的平衡分配集中进行随机化。的这个想法rerandomization由摩根和Rubin(形式化统计年鉴,2012年,40,1263年至1282年),使用处理的和对照的协变量装置作为标准来去除不平衡分配之间的马氏距离谁建议。Kallus(皇家统计学会,B系列:统计方法,2018年,80(85-112)建议将平衡分配的集合减少到最小。在这里,我们讨论了这种“最佳”重新随机化设计的含义,以推断样本中的单位以及样本中的单位是从中随机抽取的总体。我们认为,总的来说,为推论寻求最佳设计是个坏主意,因为推论通常仅反映单位随机抽样的不确定性(通常是假设的),而不是单位随机分配给治疗与对照。