Effective identification and estimation for the semiparametric measurement error model

In this paper, we study the identification and estimation of a varying coefficient partially linear model with both the error-prone and redundant covariates. By employing a finite difference method, we remove the nonparametric component from model first and propose a bias-corrected procedure for constructing an efficient parametric estimator. Then, a plug-in estimator of nonparametric function using spline approximation is constructed and the corresponding asymptotic properties are established. When the mean component of the model contains both measurement error and redundant regressors, we further identify the significant covariates by using the smoothly clipped absolute deviation (Fan and Li, 2001) penalty and show that the resultant shrinking estimators have the oracle property that is possible most optimal for variable selection. Numerical experiments and an example of application are also illustrated to evaluate the finite sample performance of our approach.