N’Guessan, A., Essai, A. and N’zi, M. (2006) An Estimation Method of the Average Effect and the Different Accident Risks When Modelling a Road Safety Measure: A Simulation Study. Computational Statistics & Data Analysis, 51, 1260-1277.
https://doi.org/10.1016/j.csda.2005.09.002

has been cited by the following article:

• TITLE: An Approximation Method for a Maximum Likelihood Equation System and Application to the Analysis of Accidents Data

  AUTHORS: Assi N’Guessan, Issa Cherif Geraldo, Bezza Hafidi

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

  JOURNAL NAME: Open Journal of Statistics, Vol.7 No.1, February 28, 2017

  ABSTRACT: 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.