In the nonlinear structural errors-in-variables model, we propose a consistent estimator of the unknown parameter using a modified least squares criterion. We give an upper bound of its rate of convergence which is strongly related to the regularity of the regression function and is generally slower than the parametric rate of convergence n-1/2. Nevertheless, the rate is of order n-1/2 for some particular analytic regression functions. For instance, when the regression function is either a polynomial function or an exponential function, we prove that our estimator achieves the parametric rate of convergence.
"Semi-Parametric Estimation in the Nonlinear Structural Errors-in-Variables Model." Ann. Statist. 29 (1) 66 - 93, February 2001. https://doi.org/10.1214/aos/996986502