Kosmidis, Ioannis and Firth, D. (David). (2009) Bias reduction in exponential family nonlinear models. Biometrika, Vol.96 (No.4). pp. 793-804. ISSN 0006-3444

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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:	Journal Article
Subjects:	Q Science > QH Natural history > QH301 Biology Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Asymptotic expansions, Nonlinear theories, Multivariate analysis, Linear models (Statistics), Estimation theory
Journal or Publication Title:	Biometrika
Publisher:	Biometrika Trust
ISSN:	0006-3444
Date:	December 2009
Volume:	Vol.96
Number:	No.4
Number of Pages:	12
Page Range:	pp. 793-804
Identification Number:	10.1093/biomet/asp055
Status:	Peer Reviewed
Publication Status:	Published
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Economic and Social Research Council (Great Britain) (ESRC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/16906

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