Bias-corrected maximum likelihood estimator of the negative binomial dispersion parameter

We derive a first-order bias-corrected maximum likelihood estimator for the negative binomial dispersion parameter. This estimator is compared, in terms of bias and efficiency, with the maximum likelihood estimator investigated by Piegorsch (1990, Biometrics46, 863-867), the moment and the maximum extended quasi-likelihood estimators investigated by Clark and Perry (1989, Biometrics45, 309-316), and a double-extended quasi-likelihood estimator. The bias-corrected maximum likelihood estimator has superior bias and efficiency properties in most instances. For ease of comparison we give results for the two-parameter negative binomial model. However, an example involving negative binomial regression is given.