Bias reduction in exponential family nonlinear models

Kosmidis, I. and Firth, D. (2009) Bias reduction in exponential family nonlinear models. Biometrika, 96 (4). pp. 793-804. ISSN 0006-3444

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Official URL: http://biomet.oxfordjournals.org/content/96/4.toc

Abstract

In Firth (1993, Biometrika) it was shown how the leading term in the asymptotic bias of the maximum likelihood estimator is removed by adjusting the score vector, and that in canonical-link generalized linear models the method is equivalent to maximizing a penalized likelihood that is easily implemented via iterative adjustment of the data. Here a more general family of bias-reducing adjustments is developed for a broad class of univariate and multivariate generalized nonlinear models. The resulting formulae for the adjusted score vector are computationally convenient, and in univariate models they directly suggest implementation through an iterative scheme of data adjustment. For generalized linear models a necessary and sufficient condition is given for the existence of a penalized likelihood interpretation of the method. An illustrative application to the Goodman row-column association model shows how the computational simplicity and statistical benefits of bias reduction extend beyond generalized linear models.

Item Type:Article
Subjects:5. Quantitative Data Handling and Data Analysis > 5.5 Regression Methods
ID Code:2086
Deposited By: L-W-S user
Deposited On:20 Feb 2012 15:10
Last Modified:20 Feb 2012 15:10

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