Admissible Bernoulli correlations

Mark Huber () and Nevena Marić ()
Additional contact information
Mark Huber: Claremont McKenna College, 850 Columbia Av
Nevena Marić: University of Missouri-St. Louis, 1 University Blvd, 311 Express Scripts Hall

Journal of Statistical Distributions and Applications, 2019, vol. 6, issue 1, 1-8

Abstract: 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.

Keywords: Bernoulli distribution; Extreme correlations; CUT polytope; 62H20; 60E05; 52B12 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1186/s40488-019-0091-5

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