Nonparametric regression function estimation for errors-in-variables models with validation data

This paper develops an estimation approach for nonparametric regression analysis with measurement error in covariates, assuming the availability of independent validation data on them, in addition to primary data on the response variable and surrogate covariates. Without specifying any error model structure between the surrogate and true covariates, we propose an estimator that integrates local linear regression and Fourier transformation methods. Under mild conditions, the consistency of the proposed estimator is established and the convergence rate is also obtained. Numerical examples show that it performs well in applications.