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Admissible Bernoulli correlations

Author

Listed:
  • Mark Huber

    (Claremont McKenna College, 850 Columbia Av)

  • Nevena Marić

    (University of Missouri-St. Louis, 1 University Blvd, 311 Express Scripts Hall)

Abstract

A multivariate symmetric Bernoulli distribution has marginals that are uniform over the pair {0,1}. Consider the problem of sampling from this distribution given a prescribed correlation between each pair of variables. Not all correlation structures can be attained. Here we completely characterize the admissible correlation vectors as those given by convex combinations of simpler distributions. This allows us to bijectively relate the correlations to the well-known CUTn polytope, as well as determine if the correlation is possible through a linear programming formulation.

Suggested Citation

  • Mark Huber & Nevena Marić, 2019. "Admissible Bernoulli correlations," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-8, December.
    • Handle: RePEc:spr:jstada:v:6:y:2019:i:1:d:10.1186_s40488-019-0091-5
    DOI: 10.1186/s40488-019-0091-5
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    References listed on IDEAS

    as
    1. N. Rao Chaganty & Harry Joe, 2006. "Range of correlation matrices for dependent Bernoulli random variables," Biometrika, Biometrika Trust, vol. 93(1), pages 197-206, March.
    2. Dias, Carlos Tadeu dos Santos & Samaranayaka, Ari & Manly, Bryan, 2008. "On the use of correlated beta random variables with animal population modelling," Ecological Modelling, Elsevier, vol. 215(4), pages 293-300.
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    Cited by:

    1. McNeil, Alexander J. & Nešlehová, Johanna G. & Smith, Andrew D., 2022. "On attainability of Kendall’s tau matrices and concordance signatures," Journal of Multivariate Analysis, Elsevier, vol. 191(C).

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