Sergiy S. Asymptotic properties of estimates of parameters of nonlinear errors-in-variables regression models

The aim of the paper is to compare the efficiencies of estimates of the parameters of measurement error models, and to construct consistent estimates in such models. Methods of the large sample theory, quasi-likelihood (the method of optimal estimation functions), the matrix perturbation theory are used. In explicit models of regression with measurement errors, efficiencies of three estimators are compared. In the sense of Loewner order for asymptotic covariance matrices, the weighted least square estimator is the most efficient, the simple score estimator is intermediate, and the estimator with corrected score is the least efficient. In implicit polynomial model, a consistent estimator is presented.