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Paper No. 10-16

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I Kosmidis and D Firth

A generic algorithm for reducing bias in parametric estimation

Date: August 2010

Abstract: A general iterative algorithm is developed for the computation of reduced-bias parameter estimates in regular statistical models using the adjusted score approach of Firth (1993, Biometrika 80, 27-38). The algorithm unifies and provides appealing new interpretation for iterative methods that have been published previously for some specific model classes. The new algorithm can usefully be viewed as a series of iterative bias corrections, thus facilitating the adjusted score approach to bias reduction in any model for which the first-order bias of the maximum likelihood estimator has already been derived. The method is tested by application to a logit-linear multiple regression model with beta-distributed responses; the results confirm the effectiveness of the new algorithm, and also reveal some important errors in the existing literature on beta regression.

Keywords: Adjusted score; Asymptotic bias correction; Beta regression; Bias reduction; Fisher scoring; Penalized likelihood; Prater gasoline data.