An Automated Profile-Likelihood-Based Algorithm for Fast Computation of the Maximum Likelihood Estimate in a Statistical Model for Crash Data
Numerical computation of maximum likelihood estimates (MLE) is one of the most common problems encountered in applied statistics. Even if there exist many algorithms considered as performing, they can suffer in some cases for one or many of the following criteria: global convergence (capacity of an...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2022-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6974166 |
| _version_ | 1798043951693824000 |
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| author | Issa Cherif Geraldo |
| author_facet | Issa Cherif Geraldo |
| author_sort | Issa Cherif Geraldo |
| collection | DOAJ |
| description | Numerical computation of maximum likelihood estimates (MLE) is one of the most common problems encountered in applied statistics. Even if there exist many algorithms considered as performing, they can suffer in some cases for one or many of the following criteria: global convergence (capacity of an algorithm to converge to the true unknown solution from all starting guesses), numerical stability (ascent property), implementation feasibility (for example, algorithms requiring matrix inversion cannot be implemented when the involved matrices are not invertible), low computation time, low computational complexity, and capacity to handle high dimensional problems. The reality is that, in practice, no algorithm is perfect, and for each problem, it is necessary to find the most performing of all existing algorithms or even develop new ones. In this paper, we consider the computing of the maximum likelihood estimate of the vector parameter of a statistical model of crash frequencies. We split the parameter vector, and we develop a new estimation algorithm using the profile likelihood principle. We provide an automatic starting guess for which convergence and numerical stability are guaranteed. We study the performance of our new algorithm on simulated data by comparing it to some of the most famous and modern optimization algorithms. The results suggest that our proposed algorithm outperforms these algorithms. |
| first_indexed | 2024-04-11T22:56:13Z |
| format | Article |
| id | doaj.art-52323b06279f4a2fb7c354eecc639221 |
| institution | Directory Open Access Journal |
| issn | 1687-0042 |
| language | English |
| last_indexed | 2024-04-11T22:56:13Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj.art-52323b06279f4a2fb7c354eecc6392212022-12-22T03:58:24ZengHindawi LimitedJournal of Applied Mathematics1687-00422022-01-01202210.1155/2022/6974166An Automated Profile-Likelihood-Based Algorithm for Fast Computation of the Maximum Likelihood Estimate in a Statistical Model for Crash DataIssa Cherif Geraldo0Département de MathématiquesNumerical computation of maximum likelihood estimates (MLE) is one of the most common problems encountered in applied statistics. Even if there exist many algorithms considered as performing, they can suffer in some cases for one or many of the following criteria: global convergence (capacity of an algorithm to converge to the true unknown solution from all starting guesses), numerical stability (ascent property), implementation feasibility (for example, algorithms requiring matrix inversion cannot be implemented when the involved matrices are not invertible), low computation time, low computational complexity, and capacity to handle high dimensional problems. The reality is that, in practice, no algorithm is perfect, and for each problem, it is necessary to find the most performing of all existing algorithms or even develop new ones. In this paper, we consider the computing of the maximum likelihood estimate of the vector parameter of a statistical model of crash frequencies. We split the parameter vector, and we develop a new estimation algorithm using the profile likelihood principle. We provide an automatic starting guess for which convergence and numerical stability are guaranteed. We study the performance of our new algorithm on simulated data by comparing it to some of the most famous and modern optimization algorithms. The results suggest that our proposed algorithm outperforms these algorithms.http://dx.doi.org/10.1155/2022/6974166 |
| spellingShingle | Issa Cherif Geraldo 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 |
| title | An Automated Profile-Likelihood-Based Algorithm for Fast Computation of the Maximum Likelihood Estimate in a Statistical Model for Crash Data |
| title_full | An Automated Profile-Likelihood-Based Algorithm for Fast Computation of the Maximum Likelihood Estimate in a Statistical Model for Crash Data |
| title_fullStr | An Automated Profile-Likelihood-Based Algorithm for Fast Computation of the Maximum Likelihood Estimate in a Statistical Model for Crash Data |
| title_full_unstemmed | An Automated Profile-Likelihood-Based Algorithm for Fast Computation of the Maximum Likelihood Estimate in a Statistical Model for Crash Data |
| title_short | An Automated Profile-Likelihood-Based Algorithm for Fast Computation of the Maximum Likelihood Estimate in a Statistical Model for Crash Data |
| title_sort | automated profile likelihood based algorithm for fast computation of the maximum likelihood estimate in a statistical model for crash data |
| url | http://dx.doi.org/10.1155/2022/6974166 |
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