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Maximum likelihood estimation for ordered expectations of correlated binary variables

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  • Wojciech Gamrot

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. Copyright The Author(s) 2013

Suggested Citation

  • Wojciech Gamrot, 2013. "Maximum likelihood estimation for ordered expectations of correlated binary variables," Statistical Papers, Springer, vol. 54(3), pages 727-739, August.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:727-739
    DOI: 10.1007/s00362-012-0458-x
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    References listed on IDEAS

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    1. Jürgen Hansohm & Xiaomi Hu, 2012. "A convergent algorithm for a generalized multivariate isotonic regression problem," Statistical Papers, Springer, vol. 53(1), pages 107-115, February.
    2. Marchand Éric & MacGibbon Brenda, 2000. "Minimax Estimation Of A Constrained Binomial Proportion," Statistics & Risk Modeling, De Gruyter, vol. 18(2), pages 129-168, February.
    3. Qian, Shixian, 1992. "Minimum lower sets algorithms for isotonic regression," Statistics & Probability Letters, Elsevier, vol. 15(1), pages 31-35, September.
    4. Hansohm, Jürgen, 2007. "Algorithms and error estimations for monotone regression on partially preordered sets," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 1043-1050, May.
    5. Ravindra K. Ahuja & James B. Orlin, 2001. "A Fast Scaling Algorithm for Minimizing Separable Convex Functions Subject to Chain Constraints," Operations Research, INFORMS, vol. 49(5), pages 784-789, October.
    6. de Leeuw, Jan & Hornik, Kurt & Mair, Patrick, 2009. "Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i05).
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    1. Ranjbar V. & Alizadeh M. & Hamedani G. G., 2018. "Extended Exponentiated Power Lindley Distribution," Statistics in Transition New Series, Statistics Poland, vol. 19(4), pages 621-643, December.
    2. V. Ranjbar & M. Alizadeh & G. G. Hademani, 2018. "Extended Exponentiated Power Lindley Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 19(4), pages 621-643, December.

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