Nonparametric Regression Function Estimation For Errors-in-Variables Models With Validation Data

This thesis develops estimation approach for nonparametric regression analysis with measurement error in covariables assuming the availability of independent valida-tion data on covariables in addition to primary data on the response variable and surro-gate covariables. Without specifying any error model structure between the surrogate and true covariables, we propose an estimator which integrates local linear regression and Fourier transformation method. An estimator combined by two local linear kernel estimators, is firstly used to calibrate the conditional expectation of unknown objective regression function given the surrogate covariates, and then the final estimator can be derived by passing a trigonometric series approach suggested by [1]. Under mild con-ditions, the consistency of the proposed estimator is established and the convergence rate is also obtained. Numerical examples show that it performs well in applications.