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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.

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  • 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: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0907.pdf
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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. 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.
    3. 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.
    4. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    5. 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.
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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. 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.
    3. 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.

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    More about this item

    Keywords

    Poisson regression model; bias; mean squared error; bias correction; random covariates;
    All these keywords.

    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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