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The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model

Received: 11 October 2014     Accepted: 3 November 2014     Published: 10 November 2014
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Abstract

During the analysis of statistical data, one of the most important steps is the estimation of the considered parameters model. The most common estimation methods are the maximum likelihood and the least squares. When the data are considered normal, there is equivalence between the two methods, so there is no privilege for one or the other method. However, if the data are not Gaussian, this equivalence is no longer valid. Also, if the normal equations are not linear, we make use of iterative methods (Newton-Raphson algorithm, Fisher, etc ...). In this work, we consider a particular case where the data are not normal and solving equations are not linear and that it leads to the equivalence of the maximum likelihood method at least squares but modified. At the end of the work, we concluded by referring to the application of this modified method for solving the equations of Liang and Zeger.

Published in Applied and Computational Mathematics (Volume 3, Issue 5)
DOI 10.11648/j.acm.20140305.22
Page(s) 268-272
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Maximum Likelihood, Linear Mixed Model, Newton-Raphson Algorithm, Weighted Least Squares

References
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    Ahsene Lanani. (2014). The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model. Applied and Computational Mathematics, 3(5), 268-272. https://doi.org/10.11648/j.acm.20140305.22

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    Ahsene Lanani. The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model. Appl. Comput. Math. 2014, 3(5), 268-272. doi: 10.11648/j.acm.20140305.22

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    AMA Style

    Ahsene Lanani. The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model. Appl Comput Math. 2014;3(5):268-272. doi: 10.11648/j.acm.20140305.22

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  • @article{10.11648/j.acm.20140305.22,
      author = {Ahsene Lanani},
      title = {The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {5},
      pages = {268-272},
      doi = {10.11648/j.acm.20140305.22},
      url = {https://doi.org/10.11648/j.acm.20140305.22},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.22},
      abstract = {During the analysis of statistical data, one of the most important steps is the estimation of the considered parameters model. The most common estimation methods are the maximum likelihood and the least squares. When the data are considered normal, there is equivalence between the two methods, so there is no privilege for one or the other method. However, if the data are not Gaussian, this equivalence is no longer valid. Also, if the normal equations are not linear, we make use of iterative methods (Newton-Raphson algorithm, Fisher, etc ...). In this work, we consider a particular case where the data are not normal and solving equations are not linear and that it leads to the equivalence of the maximum likelihood method at least squares but modified. At the end of the work, we concluded by referring to the application of this modified method for solving the equations of Liang and Zeger.},
     year = {2014}
    }
    

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    T1  - The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model
    AU  - Ahsene Lanani
    Y1  - 2014/11/10
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    AB  - During the analysis of statistical data, one of the most important steps is the estimation of the considered parameters model. The most common estimation methods are the maximum likelihood and the least squares. When the data are considered normal, there is equivalence between the two methods, so there is no privilege for one or the other method. However, if the data are not Gaussian, this equivalence is no longer valid. Also, if the normal equations are not linear, we make use of iterative methods (Newton-Raphson algorithm, Fisher, etc ...). In this work, we consider a particular case where the data are not normal and solving equations are not linear and that it leads to the equivalence of the maximum likelihood method at least squares but modified. At the end of the work, we concluded by referring to the application of this modified method for solving the equations of Liang and Zeger.
    VL  - 3
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Author Information
  • MAM Laboratory, Department of Mathematics, University of Constantine 1. Constantine 25000, Algeria

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