Efficiency comparison of two consistent estimators in nonlinear regression model with small measurement errors. (English) Zbl 1153.62015

The author studies a nonlinear measurement model where the response variable has a density belonging to the exponential family. He studies two consistent estimators: the corrected score and the quasi score one. Their relative efficiency is compared with respect to the asymptotic covariance matrices. Expansions of these matrices for small error variances are derived. It is shown that the quasi score estimator is more efficient than the corrected score one. Polynomial and Poisson regression models are studied.


62F12 Asymptotic properties of parametric estimators
62J02 General nonlinear regression