A new hybrid algorithm for maximum likelihood estimation in a model of accident frequencies

Issa Cherif  GERALDO; Tchilabalo Abozou  KPANZOU; Edoh  KATCHEKPELE

doi:10.26637/mjm1101/002

Abstract

In this paper, we are interested in the numerical computation of the constrained maximum likelihood estimator (MLE) of the parameter vector of a discrete statistical model used in statistics applied to road safety. The parameter vector is divided into two blocks: one block with the parameter of interest and the second block with secondary parameters. The MLE is the solution to a system of non-linear implicit equations difficult to solve in closed-form. To overcome this difficulty, we propose a hybrid algorithm (HA) mixing the use of a one-dimensional Newton-Raphson (NR) algorithm for the first equation of the system and a fixed-point strategy for the remaining equations. Our proposed algorithm involves no matrix inversion but it partially enjoys the quadratic convergence rate of the one-dimensional NR algorithm. We illustrate its performance on simulated data and we compare it to Newton-Raphson (NR) and quasi-Newton algorithms which are two of the most used optimization algorithms. The results suggest that our HA outperforms NR and quasi-Newton algorithms. It is accurate and converges quickly for all the starting values.

Keywords:

Statistical model, maximum likelihood, parameter estimation, road safety, Kullback-Leibler divergence

Mathematics Subject Classification:

62F10, 62F30, 62H10, 62H12, 62P99

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Issa Cherif GERALDO Laboratoire d’Analyse, de Modélisations Mathématiques et Applications (LAMMA), Département de Mathématiques, Faculté des Sciences, Université de Lomé, 1 B.P. 1515 Lomé 1, Togo.
Tchilabalo Abozou KPANZOU Département de Mathématiques, Faculté des Sciences et Techniques, Université de Kara, Kara, Togo.
Edoh KATCHEKPELE Laboratoire de Modélisation Mathématique et d’Analyse Statistique Décisionnelle (LaMMASD), Département de Mathématiques, Faculté des Sciences et Techniques, Université de Kara, Kara, Togo.

Pages: 11-24
Date Published: 01-01-2023
Vol. 11 No. 01 (2023): Malaya Journal of Matematik (MJM)

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