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A Fast and Efficient Estimation of the Parameters of a Model of Accident Frequencies via an MM Algorithm

Author

Listed:
  • Issa Cherif Geraldo
  • Edoh Katchekpele
  • Tchilabalo Abozou Kpanzou

Abstract

In this paper, we consider a multivariate statistical model of accident frequencies having a variable number of parameters and whose parameters are dependent and subject to box constraints and linear equality constraints. We design a minorization‐maximization (MM) algorithm and an accelerated MM algorithm to compute the maximum likelihood estimates of the parameters. We illustrate, through simulations, the performance of our proposed MM algorithm and its accelerated version by comparing them to Newton‐Raphson (NR) and quasi‐Newton algorithms. The results suggest that the MM algorithm and its accelerated version are better in terms of convergence proportion and, as the number of parameters increases, they are also better in terms of computation time.

Suggested Citation

  • Issa Cherif Geraldo & Edoh Katchekpele & Tchilabalo Abozou Kpanzou, 2023. "A Fast and Efficient Estimation of the Parameters of a Model of Accident Frequencies via an MM Algorithm," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnljam:v:2023:y:2023:i:1:n:3377201
    DOI: 10.1155/2023/3377201
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    References listed on IDEAS

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    1. Ravi Varadhan & Christophe Roland, 2008. "Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 335-353, June.
    2. Issa Cherif Geraldo, 2022. "An Automated Profile‐Likelihood‐Based Algorithm for Fast Computation of the Maximum Likelihood Estimate in a Statistical Model for Crash Data," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    3. Issa Cherif Geraldo & Wei-Chiang Hong, 2022. "An Automated Profile-Likelihood-Based Algorithm for Fast Computation of the Maximum Likelihood Estimate in a Statistical Model for Crash Data," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-11, October.
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