Statistical Papers

, Volume 54, Issue 3, pp 727–739

Maximum likelihood estimation for ordered expectations of correlated binary variables

Open Access
Regular Article

DOI: 10.1007/s00362-012-0458-x

Cite this article as:
Gamrot, W. Stat Papers (2013) 54: 727. doi:10.1007/s00362-012-0458-x


A multivariate binary distribution that incorporates the correlation between individual variables is considered. The availability of auxiliary information taking the form of simple ordering constraints on their expected values is assumed. The problem of constructing constraint-preserving estimates for expectations is formulated as conditional maximization of convex likelihood function for corresponding multinomial distribution with suitably chosen restrictions. Starting values for convex optimization algorithms are proposed. The proposed estimator is consistent under mild assumptions.


Binomial parameter Inequality constraints Maximum likelihood 

Mathematics Subject Classification (2000)

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of EconomicsKatowicePoland

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