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Gray codes for randomization procedures

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Abstract

We introduce a simple combinatorial scheme for systematically running through a complete enumeration of sample reuse procedures such as the bootstrap, Hartigan's subsets, and various permutation tests. The scheme is based on Gray codes which give ‘tours’ through various spaces, changing only one or two points at a time. We use updating algorithms to avoid recomputing statistics and achieve substantial speedups. Several practical examples and computer codes are given.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, One Oxford Street, 02138, Cambridge, MA, USA

    Persi Diaconis

  2. INRA, Unité de Biométrie, 2, Place Pierre Viala, 34060, Montpellier, France

    Susan Holmes

  3. Department of Statistics, Stanford University, Sequoia Hall, 94305, CA, USA

    Susan Holmes

Authors
  1. Persi Diaconis
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  2. Susan Holmes
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Diaconis, P., Holmes, S. Gray codes for randomization procedures. Stat Comput 4, 287–302 (1994). https://doi.org/10.1007/BF00156752

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