A Simple and Accurate Method for Approximate Conditional Inference Applied to Exponential Family Models

SUMMARY A simple method for approximate conditional inference is described. The methodology is applied to natural exponential family models where it is shown to provide accurate approximations to fully conditional estimates. The approximation technique can be applied much more generally than in this particular class of models. The technique depends only on the construction of certain 'projected scores' derived from higher order likelihood derivatives and their covariances and so can be used in many problems where it is relevant to control for the estimation of nuisance parameters.