Author(s)

Assi N’Guessan¹, Issa Cherif Geraldo², Bezza Hafidi³

¹Laboratoire Paul Painlevé (UMR CNRS 8524), Université de Lille 1, Villeneuve d’Ascq, France.
²Department of Mathematics and Computer science, Université Catholique de l’Afrique de l’Ouest-Unité Universitaire du Togo, Lomé, Togo.
³Department of Mathematics, Faculty of Science, University Ibn Zohr, Agadir, Morocco.

There exist many iterative methods for computing the maximum likelihood estimator but most of them suffer from one or several drawbacks such as the need to inverse a Hessian matrix and the need to find good initial approximations of the parameters that are unknown in practice. In this paper, we present an estimation method without matrix inversion based on a linear approximation of the likelihood equations in a neighborhood of the constrained maximum likelihood estimator. We obtain closed-form approximations of solutions and standard errors. Then, we propose an iterative algorithm which cycles through the components of the vector parameter and updates one component at a time. The initial solution, which is necessary to start the iterative procedure, is automated. The proposed algorithm is compared to some of the best iterative optimization algorithms available on R and MATLAB software through a simulation study and applied to the statistical analysis of a road safety measure.

Constrained Maximum Likelihood, Partial Linear Approximation, Schur’s Complement, Iterative Algorithms, Road Safety Measure, Multinomial Model

N’Guessan, A. , Geraldo, I. and Hafidi, B. (2017) An Approximation Method for a Maximum Likelihood Equation System and Application to the Analysis of Accidents Data. Open Journal of Statistics, 7, 132-152. doi: 10.4236/ojs.2017.71011.