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


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


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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    References listed on IDEAS

    1. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    2. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    3. Monta s, Antonio & Reyes, Marcelo, 1998. "Effect Of A Shift In The Trend Function On Dickey Fuller Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 14(03), pages 355-363, June.
    4. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    5. Leybourne, Stephen J. & Newbold, Paul, 2000. "BEHAVIOR OF DICKEY FULLER t-TESTS WHEN THERE IS A BREAK UNDER THE ALTERNATIVE HYPOTHESIS," Econometric Theory, Cambridge University Press, vol. 16(05), pages 779-789, October.
    6. Montañés, Antonio & Reyes, Marcelo, 1999. "The asymptotic behaviour of the Dickey-Fuller tests under the crash hypothesis," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 81-89, March.
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    Cited by:

    1. repec:sbe:breart:v:28:y:2008:i:1:a:1515 is not listed on IDEAS
    2. 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.
    3. 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.


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