Bias corrected pearson estimators for the shape parameter in gamma regression

A family of estimators based on the Pearson statistic is considered for estimation of the shape parameter in gamma regression models. Approximations to the biases of the estimators are developed and used to define a bias corrected estimator for the case of a logarithmic link for the means. The new estimator is shown to have markedly better variance and mean square error properties than existing estimators based on the Pearson statistic, in small to moderate size samples.