Efficiency comparison of two consistent estimators in nonlinear regression model with small measurement errors

We study a nonlinear measurement model where the response variable has a density belonging to the exponential family. We consider two consistent estimators: Corrected Score (CS) and Quasi Score (QS) ones. Their relative e?ciency is compared with respect to asymptotic covariance matrices. We derive expansions of these matrices for small error variances. It is shown that the QS estimator is more e?cient than the CS one. The polynomial and Poisson regression models are studied in more detail.