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

Ahsene Lanani

doi:doi:10.11648/j.acm.20140305.22

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

Ahsene Lanani

Published in Applied and Computational Mathematics (Volume 3, Issue 5)

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 However, if the data are not Gaussian, this equivalence is no longer valid.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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APA Style

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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ACS 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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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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TY  - JOUR
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
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.22
DO  - 10.11648/j.acm.20140305.22
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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
IS  - 5
ER  -

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Author Information

Ahsene Lanani

MAM Laboratory, Department of Mathematics, University of Constantine 1. Constantine 25000, Algeria

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APA Style

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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ACS 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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.22
DO  - 10.11648/j.acm.20140305.22
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 268
EP  - 272
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140305.22
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
IS  - 5
ER  -

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