On optimal rerandomization designs

Per Johansson Uppsala University and IFAU, Uppsala, Sweden; Tsinghua University, Beijing, China Donald B. Rubin Tsinghua University, Beijing, China Mårten Schultzberg Uppsala University, Uppsala, Sweden

Statistics Theory and Methods mathscidoc:2206.33003

Journal of the Royal Statistical Society: Series B (Statistical Methodology), 83, (2), 395-403, 2021.4
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.
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  title={On optimal rerandomization designs},
  author={Per Johansson, Donald B. Rubin, and Mårten Schultzberg},
  booktitle={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
Per Johansson, Donald B. Rubin, and Mårten Schultzberg. On optimal rerandomization designs. 2021. Vol. 83. In Journal of the Royal Statistical Society: Series B (Statistical Methodology). pp.395-403. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220621170537647476432.
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