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

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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File URL: http://www.uvic.ca/socialsciences/economics/assets/docs/econometrics/ewp0907.pdf
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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0907.

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Length: 17 pages
Date of creation: 22 Sep 2009
Date of revision:
Handle: RePEc:vic:vicewp:0907
Note: ISSN 1485-6441
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Web page: http://web.uvic.ca/econ

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  1. Qian Chen & David E. Giles, 2009. "Finite-Sample Properties of the Maximum Likelihood Estimator for the Binary Logit Model With Random Covariates," Econometrics Working Papers 0906, Department of Economics, University of Victoria.
  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. Gourieroux Christian & Monfort Alain & Trognon A, 1982. "Pseudo maximum lilelihood methods : applications to poisson models," CEPREMAP Working Papers (Couverture Orange) 8203, CEPREMAP.
  4. 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.
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