Robust and consistent estimation of nonlinear errors-in-variables models

This paper considers the consistent estimation of nonlinear errors-in-variables models. It adopts the functional modeling approach by assuming that the true but unobserved regressors are random variables but making no parametric assumption on the distribution from which the latent variables are drawn. This paper shows how the information extracted from the replicate measurements can be used to identify and consistently estimate a general nonlinear errors-in-variables model. The identification is established through characteristic functions. The estimation procedure involves nonparametric estimation of the conditional density of the latent variables given the measurements using the identification results at the first stage, and at the second stage, a semiparametric nonlinear least-squares estimator is proposed. The consistency of the proposed estimator is also established. Finite sample performance of the estimator is investigated through a Monte Carlo study.