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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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number
0907.
Length: 17 pages Date of creation: 22 Sep 2009 Date of revision: Handle: RePEc:vic:vicewp:0907
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