BIAS REDUCTION OF MAXIMUM-LIKELIHOOD-ESTIMATES

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 familie s with canonical parameterization the effect is to penalize the likeli hood by the Jeffreys invariant prior. In binomial logistic models, Poi sson log linear models and certain other generalized linear models, th e Jeffreys prior penalty function can be imposed in standard regressio n software using a scheme of iterative adjustments to the data.