IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v54y2013i3p727-739.html
   My bibliography  Save this article

Maximum likelihood estimation for ordered expectations of correlated binary variables

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-012-0458-x
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00362-012-0458-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Qian, Shixian, 1992. "Minimum lower sets algorithms for isotonic regression," Statistics & Probability Letters, Elsevier, vol. 15(1), pages 31-35, September.
    2. 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.
    3. Marchand Éric & MacGibbon Brenda, 2000. "Minimax Estimation Of A Constrained Binomial Proportion," Statistics & Risk Modeling, De Gruyter, vol. 18(2), pages 129-168, February.
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ranjbar V. & Alizadeh M. & Hamedani G. G., 2018. "Extended Exponentiated Power Lindley Distribution," Statistics in Transition New Series, Polish Statistical Association, 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stout, Quentin F., 2008. "Unimodal regression via prefix isotonic regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 289-297, December.
    2. Johannes Friedrich & Pengcheng Zhou & Liam Paninski, 2017. "Fast online deconvolution of calcium imaging data," PLOS Computational Biology, Public Library of Science, vol. 13(3), pages 1-26, March.
    3. Cui, Zhenyu & Lee, Chihoon & Zhu, Lingjiong & Zhu, Yunfan, 2021. "Non-convex isotonic regression via the Myersonian approach," Statistics & Probability Letters, Elsevier, vol. 179(C).
    4. Nguyen, Kien Trung & Hung, Nguyen Thanh, 2021. "The minmax regret inverse maximum weight problem," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    5. repec:jss:jstsof:39:i06 is not listed on IDEAS
    6. Bucarey, Víctor & Labbé, Martine & Morales, Juan M. & Pineda, Salvador, 2021. "An exact dynamic programming approach to segmented isotonic regression," Omega, Elsevier, vol. 105(C).
    7. Asfha, Huruy & Hu, Xiaomi, 2023. "An algorithm for a pseudo RMLE under simple tree multivariate order restriction," Statistics & Probability Letters, Elsevier, vol. 202(C).
    8. Dimitriadis, Timo & Gneiting, Tilmann & Jordan, Alexander I. & Vogel, Peter, 2024. "Evaluating probabilistic classifiers: The triptych," International Journal of Forecasting, Elsevier, vol. 40(3), pages 1101-1122.
    9. Chathura Siriwardhana & K. B. Kulasekera & Somnath Datta, 2018. "Flexible semi-parametric regression of state occupational probabilities in a multistate model with right-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 464-491, July.
    10. David Wu & Viet Hung Nguyen & Michel Minoux & Hai Tran, 2022. "Optimal deterministic and robust selection of electricity contracts," Journal of Global Optimization, Springer, vol. 82(4), pages 993-1013, April.
    11. Fang, Fang & Chen, Yuanyuan, 2019. "A new approach for credit scoring by directly maximizing the Kolmogorov–Smirnov statistic," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 180-194.
    12. Keshvari, Abolfazl & Kuosmanen, Timo, 2013. "Stochastic non-convex envelopment of data: Applying isotonic regression to frontier estimation," European Journal of Operational Research, Elsevier, vol. 231(2), pages 481-491.
    13. Barragán, Sandra & Fernández, Miguel & Rueda, Cristina & Peddada, Shyamal, 2013. "isocir: An R Package for Constrained Inference Using Isotonic Regression for Circular Data, with an Application to Cell Biology," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i04).
    14. Jelsema, Casey M. & Peddada, Shyamal D., 2016. "CLME: An R Package for Linear Mixed Effects Models under Inequality Constraints," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 75(i01).
    15. Park, Chul Gyu, 1998. "Least squares estimation of two functions under order restriction in isotonicity," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 97-100, January.
    16. David Conde & Miguel A. Fernández & Cristina Rueda & Bonifacio Salvador, 2021. "Isotonic boosting classification rules," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(2), pages 289-313, June.
    17. Oleg Burdakov & Oleg Sysoev, 2017. "A Dual Active-Set Algorithm for Regularized Monotonic Regression," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 929-949, March.
    18. Ravindra K. Ahuja & Dorit S. Hochbaum & James B. Orlin, 2003. "Solving the Convex Cost Integer Dual Network Flow Problem," Management Science, INFORMS, vol. 49(7), pages 950-964, July.
    19. Mankad, Shawn & Michailidis, George & Banerjee, Moulinath, 2015. "Threshold Value Estimation Using Adaptive Two-Stage Plans in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i03).
    20. Liao, Xiyue & Meyer, Mary C., 2014. "coneproj: An R Package for the Primal or Dual Cone Projections with Routines for Constrained Regression," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(i12).
    21. Eduardo L. Montoya & Wendy Meiring, 2016. "An F-type test for detecting departure from monotonicity in a functional linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 322-337, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:727-739. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.