Estimation in the nonlinear errors-in-variables model

Abstract

In the nonlinear structural errors-in-variables model we propose a consistent estimator of the unknown parameter, using a modified least squares criterion. Its rate of convergence strongly related to the regularity of the regression function, is generally slower than the parametric rate of convergence n −1/2. Nevertheless, it is of order (log n) r/√ n, r > 0, for some analytic regression functions.