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In this paper we derive general formulae for first-order biases of maximum likelihood estimates of the linear parameters, linear predictors, the dispersion parameter and fitted values in generalized linear models. These formulae may be implemented in the GLIM program to compute bias-corrected maximum likelihood estimates to order n-1, where n is the sample size, with minimal effort by means of a supplementary weighted regression. For linear logistic models it is shown that the asymptotic bias vector of β̂ is almost collinear with β. The approximate formula β p/m+ for the bias of betâ in logistic models, where p = dim(β) and m+ = Σ mi is the sum of the binomial indices, is derived and checked numerically.
Series B (Statistical Methodology) of the Journal of the Royal Statistical Society started out simply as the Supplement to the Journal of the Royal Statistical Society in the Society's centenary year of 1934. The journal now publishes high quality papers on the methodological aspects of statistics. The objective of papers is to contribute to the understanding of statistical methodology and/or to develop and improve statistical methods. JSTOR provides a digital archive of the print version of Journal of the Royal Statistical Society, Series B: Statistical Methodology. The electronic version of Journal of the Royal Statistical Society, Series B: Statistical Methodology is available at http://www.blackwell-synergy.com/servlet/useragent?func=showIssues&code;=rssb. Authorized users may be able to access the full text articles at this site.
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Journal of the Royal Statistical Society. Series B (Methodological)
© 1991 Royal Statistical Society