Statistical estimation in varying coefficient models with surrogate data and validation sampling

Varying coefficient error-in-covariables models are considered with surrogate data and validation sampling. Without specifying any error structure equation, two estimators for the coefficient function vector are suggested by using the local linear kernel smoothing technique. The proposed estimators are proved to be asymptotically normal. A bootstrap procedure is suggested to estimate the asymptotic variances. The data-driven bandwidth selection method is discussed. A simulation study is conducted to evaluate the proposed estimating methods.