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Finite-Sample Properties of the Maximum Likelihood Estimator for the Poisson Regression Model With Random Covariates

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Abstract

We examine the small-sample behaviour of the maximum likelihood estimator for the Poisson regression model with random covariates. Analytic expressions for the first-order bias and second-order mean squared error for this estimator are derived, and we undertake some numerical evaluations to illustrate these results for the single covariate case. The properties of the bias-adjusted maximum likelihood estimator, constructed by subtracting the estimated first-order bias from the original estimator, are investigated in a Monte Carlo experiment. Correcting the estimator for its first-order bias is found to be effective in the cases considered, and we recommend its use when the Poisson regression model is estimated by maximum likelihood with small samples.

Suggested Citation

  • Qian Chen & David E. Giles, 2009. "Finite-Sample Properties of the Maximum Likelihood Estimator for the Poisson Regression Model With Random Covariates," Econometrics Working Papers 0907, Department of Economics, University of Victoria.
  • Handle: RePEc:vic:vicewp:0907
    Note: ISSN 1485-6441
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    File URL: http://www.uvic.ca/socialsciences/economics/assets/docs/econometrics/ewp0907.pdf
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    References listed on IDEAS

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    1. Qian Chen & David Giles, 2012. "Finite-sample properties of the maximum likelihood estimator for the binary logit model with random covariates," Statistical Papers, Springer, vol. 53(2), pages 409-426, May.
    2. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    3. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    4. Cameron, A Colin & Trivedi, Pravin K, 1986. "Econometric Models Based on Count Data: Comparisons and Applications of Some Estimators and Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(1), pages 29-53, January.
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    Cited by:

    1. David E. Giles & Hui Feng, 2009. "Almost Unbiased Estimation of the Poisson Regression Model," Econometrics Working Papers 0909, Department of Economics, University of Victoria.
    2. David E Giles & Hui Feng, 2011. "Reducing the bias of the maximum likelihood estimator for the Poisson regression model," Economics Bulletin, AccessEcon, vol. 31(4), pages 2933-2943.
    3. Qian Chen & David Giles, 2012. "Finite-sample properties of the maximum likelihood estimator for the binary logit model with random covariates," Statistical Papers, Springer, vol. 53(2), pages 409-426, May.

    More about this item

    Keywords

    Poisson regression model; bias; mean squared error; bias correction; random covariates;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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