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Second-order biases of maximum likelihood estimates in overdispersed generalized linear models

Author

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  • Cordeiro, Gauss M.
  • Botter, Denise A.

Abstract

In this paper, we derive general formulae for second-order biases of maximum likelihood estimates in overdispersed generalized linear models, thus generalizing results by Cordeiro and McCullagh (J. Roy. Statist. Soc. Ser. B 53 (1991) 629), and Botter and Cordeiro (Statist. Comput. Simul. 62 (1998) 91). Our formulae cover many important and commonly used models and are easily implemented by means of supplementary weighted linear regressions. They are also simple enough to be used algebraically to obtain several closed-form expressions in special models. The practical use of such formulae is illustrated in a simulation study.

Suggested Citation

  • Cordeiro, Gauss M. & Botter, Denise A., 2001. "Second-order biases of maximum likelihood estimates in overdispersed generalized linear models," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 269-280, December.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:3:p:269-280
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    Cited by:

    1. Barreto-Souza, Wagner & Vasconcellos, Klaus L.P., 2011. "Bias and skewness in a general extreme-value regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1379-1393, March.
    2. Artur J. Lemonte & Germán Moreno–Arenas, 2020. "Improved Estimation for a New Class of Parametric Link Functions in Binary Regression," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 84-110, May.
    3. Cordeiro, Gauss M., 2008. "Corrected Maximum Likelihood Estimators in Linear Heteroskedastic Regression Models," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 28(1), May.
    4. Patriota, Alexandre G. & Lemonte, Artur J., 2009. "Bias correction in a multivariate normal regression model with general parameterization," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1655-1662, August.

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