Bias-reduced maximum likelihood estimation of the zero-inflated Poisson distribution

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We investigate the small-sample quality of the maximum likelihood estimators (MLE) of the parameters of a zero-inflated Poisson distribution (ZIP). The finite-sample bias of the MLE is determined to O(n−1) using an analytic bias-reduction methodology based on the work of Cox and Snell (1968 Cox, D.R., Snell, E.J. (1968). A general definition of residuals. J. Royal Stat. Soc. Ser. B 30:248–275. [Google Scholar]) and Cordeiro and Klein (1994 Cordeiro, G.M., Klein, R. (1994). Bias correction in ARMA models. Stat. Prob. Lett. 19:169–176.[Crossref], [Web of Science ®] , [Google Scholar]). Monte Carlo simulations show that the MLEs have very small percentage biases for this distribution, but the analytic bias-reduction methods essentially eliminate the bias without adversely affecting the mean-squared errors of the estimators. The analytic adjustment compares favorably with the parametric bootstrap bias-corrected estimator, in terms of bias reduction itself, as well as with respect to mean-squared error and Pitman’s nearness measure.