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A geometric approach to a class of optimization problems concerning exchangeable binary variables

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  • Di Cecco, Davide

Abstract

In [Zaigraev, A., Kaniovski, S., 2010. Exact bounds on the probability of at least k successes in n exchangeable Bernoulli trials as a function of correlation coefficients. Statist. Probab. Lett. 80, 1079-1084] the authors present sharp bounds for the probability Rk,n of having k successes out of n exchangeable Bernoulli trials, as a function of the marginal probability of success. The result is obtained by linear programming arguments. In this paper we develop further the result utilizing a geometrical approach to the problem, and find sharp bounds for Rk,n given the marginal probability of success and the correlation among the exchangeable variables.

Suggested Citation

  • Di Cecco, Davide, 2011. "A geometric approach to a class of optimization problems concerning exchangeable binary variables," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 411-416, March.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:3:p:411-416
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    References listed on IDEAS

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    1. Kaniovski, Serguei, 2009. "An invariance result for homogeneous juries with correlated votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 213-222, March.
    2. Zaigraev, Alexander & Kaniovski, Serguei, 2010. "Exact bounds on the probability of at least k successes in n exchangeable Bernoulli trials as a function of correlation coefficients," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1079-1084, July.
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