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Covariance matrix of the bias-corrected maximum likelihood estimator in generalized linear models

Author

Listed:
  • Gauss Cordeiro
  • Denise Botter
  • Alexsandro Cavalcanti
  • Lúcia Barroso
Abstract
For the first time, we obtain a general formula for the $$n^{-2}$$ asymptotic covariance matrix of the bias-corrected maximum likelihood estimators of the linear parameters in generalized linear models, where $$n$$ is the sample size. The usefulness of the formula is illustrated in order to obtain a better estimate of the covariance of the maximum likelihood estimators and to construct better Wald statistics. Simulation studies and an application support our theoretical results. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Gauss Cordeiro & Denise Botter & Alexsandro Cavalcanti & Lúcia Barroso, 2014. "Covariance matrix of the bias-corrected maximum likelihood estimator in generalized linear models," Statistical Papers, Springer, vol. 55(3), pages 643-652, August.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:643-652
    DOI: 10.1007/s00362-013-0514-1
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    References listed on IDEAS

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    1. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    2. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    3. Cordeiro, Gauss M., 2004. "Second-order covariance matrix of maximum likelihood estimates in generalized linear models," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 153-160, January.
    4. Ferrari, Silvia L. P. & Botter, Denise A. & Cordeiro, Gauss M. & Cribari-Neto, Francisco, 1996. "Second- and third-order bias reduction for one-parameter family models," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 339-345, November.
    5. Audrey Cysneiros & Katya Rodrigues & Gauss Cordeiro & Silvia Ferrari, 2010. "Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models," Statistical Papers, Springer, vol. 51(2), pages 273-284, June.
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