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

Abstract

We examine the small-sample behaviour of the maximum likelihood estimator for the Poisson regression model with random covariates. Analytic expressions for the second-order bias and mean squared error 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 are investigated in a Monte Carlo experiment. Correcting the estimator for its second-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.

Keywords:

• Bias
• Bias correction
• Mean squared error
• Poisson regression model
• Random covariates

Mathematics Subject Classification:

• 62F10
• 62J12
• 62P20