Firth, David Bias reduction of maximum likelihood estimates. (English) Zbl 0769.62021 Biometrika 80, No. 1, 27-38 (1993). Summary: It is shown how, in regular parametric problems, the first-order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function. In exponential families with canonical parameterization the effect is to penalize the likelihood by the Jeffreys invariant prior. In binomial logistic models, Poisson log linear models and certain other generalized linear models, the Jeffreys prior penalty function can be imposed in standard regression software using a scheme of iterative adjustments to the data. Cited in 20 ReviewsCited in 201 Documents MSC: 62F10 Point estimation 62J12 Generalized linear models (logistic models) Keywords:asymptotic bias; biased estimating equations; logistic regression; modified score; penalized likelihood; shrinkage; first-order term; asymptotic bias of maximum likelihood estimates; score function; exponential families; canonical parameterization; Jeffreys invariant prior; binomial logistic models; Poisson log linear models; generalized linear models; Jeffreys prior penalty function; iterative adjustments Software:brglm2 PDFBibTeX XMLCite \textit{D. Firth}, Biometrika 80, No. 1, 27--38 (1993; Zbl 0769.62021) Full Text: DOI Link