Modified almost unbiased two-parameter estimator for the Poisson regression model with an application to accident data

• Mustafa I. Alheety ^[1] ; Muhammad Qasim ^[3] ; Kristofer Månsson ^[3] ; B. M. Golam Kibria ^[2]
  1. [1] University of Anbar

     University of Anbar

     Irak

     
  2. [2] Florida International University

     Florida International University

     Estados Unidos

     
  3. [3] Jönköping University, Suecia

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• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 45, Nº. 2, 2021, págs. 121-142
• Idioma: inglés
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• Resumen

  • Due to the large amount of accidents negatively affecting the wellbeing of the survivors and their families, a substantial amount of research is conducted to determine the causes of road accidents. This type of data come in the form of non-negative integers and may be modelled using the Poisson regression model. Unfortunately, the commonly used maximum likelihood estimator is unstable when the explanatory variables of the Poisson regression model are highly correlated. Therefore, this paper proposes a new almost unbiased estimator which reduces the instability of the maximum likelihood estimator and at the same time produce smaller mean squared error. We study the statistical properties of the proposed estimator and a simulation study has been conducted to compare the performance of the estimators in the smaller mean squared error sense. Finally, Swedish traffic fatality data are analyzed to show the benefit of the proposed method.