Abstract
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.
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Acknowledgments
The work was partially supported by the Grant No NN111 558540 from the Ministry of Science and Higher Education. The author is indebted to two anonymous referees for helpful comments that led to generalization of the consistency theorem and improvement of the manuscript.
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Gamrot, W. Maximum likelihood estimation for ordered expectations of correlated binary variables. Stat Papers 54, 727–739 (2013). https://doi.org/10.1007/s00362-012-0458-x
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DOI: https://doi.org/10.1007/s00362-012-0458-x
Keywords
- Binomial parameter
- Inequality constraints
- Maximum likelihood
Mathematics Subject Classification (2000)
- 62F30