Adjusted profile estimating function

In settings where the full probability model is not specified, consider a general estimating function $g(\theta, \lambda; y)$ that involves not only the parameters of interest, $\theta$, but also some nuisance parameters, $\lambda$. We consider methods for reducing the effects on g of fitting nuisance parameters. We propose Cox-Reid-type adjustment to the profile estimating function, $g(\theta, \hat\lambda_\theta; y)$, that reduces its bias by two orders. Typically, only the first two moments of the response variable are needed to form the adjustment. Important applications of this method include the estimation of the pairwise association and main effects in stratified, clustered data and estimation of the main effects in a matched pair study. A brief simulation study shows that the proposed method considerably reduces the impact of the nuisance parameters.