Nonparametric regression function estimation with surrogate data and validation sampling

This paper develops estimation approaches for nonparametric regression analysis with surrogate data and validation sampling when response variables are measured with errors. Without assuming any error model structure between the true responses and the surrogate variables, a regression calibration kernel regression estimate is defined with the help of validation data. The proposed estimator is proved to be asymptotically normal and the convergence rate is also derived. A simulation study is conducted to compare the proposed estimators with the standard Nadaraya–Watson estimators with the true observations in the validation data set and the complete observations, respectively. The Nadaraya–Watson estimator with the complete observations can serve as a gold standard, even though it is practically unachievable because of the measurement errors.