The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model
Applied and Computational Mathematics
Volume 3, Issue 5, October 2014, Pages: 268-272
Received: Oct. 11, 2014; Accepted: Nov. 3, 2014; Published: Nov. 10, 2014
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Ahsene Lanani, MAM Laboratory, Department of Mathematics, University of Constantine 1. Constantine 25000, Algeria
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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 However, if the data are not Gaussian, this equivalence is no longer valid.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.
Maximum Likelihood, Linear Mixed Model, Newton-Raphson Algorithm, Weighted Least Squares
To cite this article
Ahsene Lanani, The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model, Applied and Computational Mathematics. Vol. 3, No. 5, 2014, pp. 268-272. doi: 10.11648/j.acm.20140305.22
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